I have some approved edits, which should increase my reputation.
The reputation from approved edits is capped at 1000:
You gain reputation when:
suggested edit is accepted: +2 (up to +1000 total per user)
Source What is reputation? How do I earn (and lose) it? - Help Center - Super User
I wanted to say thank you to him, so I thought to give 5 points bounty to him.
A bounty isn't intended as a way to say "thank you" for an answer. So the bounty system is designed to prevent small amounts of reputation from being transferred.
I found that I can't give bounty until I have 75 reputation nor can I give less than 50 point bounty.
You should ...
A single up vote on an answer is worth 10 reputation to the receiver, and on a question it is worth 5 reputation.
Giving an up vote is completely free to you, and is more of a bonus than a single bounty of 5 reputation.
As bounties can only be given to answers that makes your proposed 5 rep bounty worth less than a single upvote.
There is no reason to ...
“I see many upvotes not counted, only 35 are considered.”
You have been repcapped:
You can earn a maximum of 200 reputation per day from the combination of upvotes, downvotes and suggested edits. But Bounty awards, accepted answers, and association bonuses are not subject to this daily reputation limit.
Source What is reputation? How do I earn (and lose)...
Meta sites still track reputation internally - it's just never displayed anywhere. For example, your "meta rep" right now is 23.
So you can still earn badges related to reputation, as odd as that may seem.
See also: https://meta.stackoverflow.com/questions/251249/mortarboard-continues-to-be-awarded-on-meta-stack-overflow