There are a few things to keep in mind when you start playing this game.
1. You have to keep a good eye on your funds
Healing can be expensive if you have a bunch of wounded sleepers, when you have just caught a sleeper, even if they are slightly injured or used some skills in their battle against you, it will bump off the cost of healing. You can keep it from adding to the cost by either deleting them at the terminal, or transferring their skills to another unit.
2. There is a mini map button
Apparently they tell you this after you reach the mansion, but not before that for the entire prior segments. For computer users, the default input is alt to activate it, and it does make navigation much easier than constantly opening the map every 10 steps. You do need to have battery on your phone to make use of it though, bringing us to the next point.
3. Keep an eye on your power
This is very important! If you run out of power, all functions on your phone will stop working. This includes party members, the map, and hijacking monsters (If I remember correctly). If you don't have any backup batteries, you want to get your hands on a magic fabric, so you can get out of there if the situation turns dire. If you do run out of battery and use a backup battery, then you will need to manually put all your party members back into place if you want them to be present in battle. Otherwise, you will enter the next battle without any party members, which, even with a higher level character, can make the battles difficult to deal with. Also, I didn't mention this before, but the strength and number of party members alters the amount of power drained. The less members, the lower the power use. If you have a full party of lower level members than you, the power cost won't be too much, if they are higher level though, it will have a heavy cost, even with the passive power use reduction.

This part is meant to help understand different parts of the terminals that are now present around the 'over-world' and in 'dungeons'.

To start, Fusions.
In short, it is the act of fusing two sleepers together to make a new sleeper. The result being a version of the new sleeper with any skills that you choose to pass on to it. You are limited to the sleepers normal empty slots though, you can't overwrite the sleepers original skills in this menu. I should mention that this method also lets you transfer otherwise nontransferable skills, like the specials. Some examples you could try is fusing Orin with another sleeper, and giving the resulting sleeper [cat scratch fever]. This can be done over and over again, and can result in giving special skills to characters that can be used in another fusion, and then do it again. This is an example.

As far as I know, it will pull from the database versions of the sleepers you save, so any sleepers with extra skills fused to them will be pulled for fusions using those sleepers. If you have one in your party though, that one will be used. So if you don't want to lose the skills you put on that character, make sure to save them first. Be aware though, the database only saves two copies. The original sleeper, and the saved version of the sleeper. There are also a few sleepers you can only get from the fuse menu. I could be wrong, but you can't seem to hijack normal Kemada, You can use them in the database to transfer over skills easily by fusing into one. Since you probably won't be using them in battle anyways. They are also cheap to make, so if you transfer over some useful skills to them, you can buy one cheap and use them to transfer some good skills to other units.
- The sacrifice menu is also under this, but all it seems to do is transfer exp to the sleeper selected. It can be good if you are training up some weaker sleepers, but if you do this, you can't transfer over any skills.

Then there is skill transfer menu.
In short, it transfers some of the skills to the base sleeper from the second selection. Unlike in fusions, this one can overwrite skills that are present, but you can't transfer over the special skills. So if you already transferred the specials you want on the character, you can fuse the rest of the skills you are missing in that characters build. You can also give Sumireko some more skills with this menu.

Also, there is affinity transfer.
Which I did use in the last image. I should mention, as far as I know, it can only change resistances and weaknesses for Sumireko. It can't be used on changing other sleepers affinity. The plus signs on the fire affinity for the image above means that when attacked with that element, they will gain health instead of loose it. As far as I know, your defense buffs don't change the health recovered, but I don't know that with certainty. I will say though, for the first area, this affinity setup is very helpful for Sumireko, especially if you have party members with fire immunity and Utsho in your party. [Red sun over paradise] is very helpful for self recovery, and striking foes weak to fire.

Sorry, that was a bit off topic. I'll get back to my explanation.
The plus symbols under the element mean they recover health when hit with the element
The white shield means it fully blocks damage you take from that element
The white outline around a black shield means it reduces that element's damage taken
The dash symbol means it's neutral, it doesn't do extra or less damage
The exclamation mark means that you will take increased damage when attacked with that element

The database
Shows all the sleepers you have hijacked/caught. It can also can save any changes made to them. The original save is automatically made when you first catch the sleeper. The saved one can only be made from the terminal. Keep in mind, every time you save it overwrites your past save for the sleeper. So if they have skills you want on the saved version, but not on your current version, you need to choose which setup to keep. If you want to load the setup you had before, you need to delete your current one, or sacrifice them to another one to give them experience and remove them from your party.
As a side note: You can only have one of each sleeper in your party at a time, but you do have a party size limit. If you go past it, you can't record any more sleepers. There is some upgrades you can get to increase party size, but you can't remove sleepers away from a terminal.

Also, I mentioned this before, but it is helpful so I will say it again, you can fuse some monsters into the database that can't be gotten otherwise, you can add useful skills to them to use as fusion material that is cheap to afford.

I am just going to share my personal method for out of battle healing. It was to get a very high level sleeper through grinding money for hijack upgrades, and then heading to a high level area to catch a sleeper with a very high MP and MAG. I will use Shion for my example since you can also fuse for her early on if you farm exp for a very long time. I don't recommend that though, since you can use weaker monsters for this just as easily. You can do this with anyone that you can catch with a high MAG and MP. If you give them a skill with a healing effect, they can do a bunch of healing between battles without affecting your battery cost, since the battery cost is based on your active party, and not your passive members. On a side note, Shion is very hard to get to in the game, but she can use Medi to do a large amount of healing without too much issue out of battle. Giving her status removal skills would also help if you are exploring the poison forest, because it can save you some money on antidotes. You can use Ellen if you find her in the forest as an easier to find alternative. Hers isn't as high immediately, but she is easier to get in comparison. Reimu and Marisa also can do this, but I hadn't tried that since I use them more in fights with the Byakuren I showed in another section, since her [Without judgement] skill is a good in battle heal when there are more human active party members.

I could be wrong on the cost, but as long as you don't rely on skill healing out of battle too long, the cost for healing can be somewhat manageable and you should have enough MP on your healer to last for a good while. You do need to make sure you hijack some sleepers for money to maintain your money though. One easy method is going to Entei and hunting Tewi, since their money from hijack is pretty good, if I remember correctly it was 1155? You can also grind first aid kits from Erin's item hijack and Tewi also gives magic fabric from hers.

While I did say before that having to many members could be detrimental to catching new sleepers since it would use a bunch of slots, if you minimize your necessary sleepers to just a few members, you can use the rest to catch new sleepers.