The first impression of these spells as a whole is that they are a good start and fit the theme you are interested in. That is, I think there are a few points worth mentioning. Let's go over every single spell in detail.
This is basically a situation triggered version of misty stepThis is a second level spell. But yours is a reaction instead of a bonus action and brings a surge of damage. It is also similar to the sixth level of the monk Way of Shadow Shadowstep How is it a limited teleport?
In terms of strength, I think this spell is fine if you lean slightly to the more powerful side for a first-level spell. But given the limitations, it would probably be too weak on the second level.
A possible useful exploit would be if someone was able to pour revive If you took this spell, an instant teleport to the side of a fallen ally could be useful, but no game interruption.
Let the dying go
This spell is a bit overwhelmed, especially during upcasting. The damage percentage is okay, as damage from the same source can not be stacked, and it's pretty cool to trigger extra damage each time someone dies nearby. The broken part is the unfocused, unlimited continuous healing.
With this spell, you could hit a bunch of enemies and cast spells fireball centered on yourself, assuming you kill at least a few of them what you want to win Hitpoints of it. This is clearly an overpowering combination.
The next saying I could find is Vampiric touch A third level spell that only takes 1 minute to complete and requires concentration. I would consider rewriting this saying with this as a starting point, at least with the reduced duration.
This is a nice saying, but it requires a little work. I think it would be reasonably balanced with a few improvements.
First, I think you need to save against the effects of the spell. A melee attack is much easier than destroying a powerful enemy. If you make an attack roll and do not save until the end of your turn, this effect is almost automatically successful and extremely effective.
By preventing spells until the end of their turn, they can not cast a spell over what your party is doing, or what is probably their best skill for a full turn. A single roll of this effect gives your group 2 rounds to attack the enemy with no chance of it bouncing back.
Second, simplify the mechanics. Currently, this spell triggers multiple throws per turn. an attack roll, a concentration test for the spell effect, a concentration check for the damage taken, and then the spell at the end of your turn. A single Save per turn and clearer effects would be an improvement.
Third, it's a bit too weak to call this melee Disperse magic, I suppose the car hit was a compromise, but I think it's too complex and would only give it an area instead. 30, 60 or even 120ft to match Disperse magic would be fine.
Finally, add a duration. You have failed to specify a duration, but I would suggest that 1 minute would be balanced, though it is unlikely that the spell will ever last the entire duration.
With these changes, the spell would look something like this:
Level 3: Forgive, 1 Action
Duration: 1 minute
You are sending out a wave of psychic dissonance to a creature that you can see within easy reach. The target must perform an intelligence rescue. In the case of a failed save, target 2W8 suffers mental damage, its concentration (if concentrated) is disrupted and it can not cast spells for the duration. If successfully saved, the target suffers half of the damage and is otherwise untouched. You can repeat this action at the end of each turn. If successful, the spell ends.
This version is still not perfect and probably needs more balance optimizations to get it right, but it's a lot easier while achieving the same effects.
One last word
A note that can apply to any of these spells and your entire topic in general. Spells and abilities that benefit from death, especially those like Let the dying go can quickly turn the tide of battles and lead to death spirals. When used by a PC this is not terrible and may even be desirable at times, but if a DM intends to use spells like this against the players, they should be careful with TPKs.
Watch out for these spells, which play down a few bouts during your play test, and make adjustments if necessary. Even individually balanced spells can get out of hand when a player cleverly combines them.