Ask @arcadiagt5:

People you may like

Want to make more friends? Try this: Tell us what you like and find people with the same interests. Try this: + add more interests + add your interests

How would you introduce yourself on dating app?

Politely, after reading her profile, and referencing common interests.
Dating apps have never really interested me, but after hearing so much about the toxicity that goes on there I'm tempted to run an experiment on say Ok Cupid.
Just be decent, starting with the introduction approach above, generally avoiding being crude, and moving on to gracefully taking no for an answer
Just to see what sort of reactions that would get.

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What's the best way to apologize?

Truly own your mistake and not quibble about the impact or assign blame to the victim by using a construct like "I'm sorry if you were offended."
No. The right way to do it is "I was wrong and I'm sorry I hurt/offended you." In that form there's nothing on the victim, you are owning your mistake.
That's the critical point but John @scalzi has a much better guide here:

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