Hi, I have 2 questions
1, I will apply for British citizenship this year. It needs "good character" by Home Office when applying for a British citizen. Will this criminal record affect me when I apply for British citizenship?
We can't say. If you are convicted, you will need to speak to a specialist immigration solicitor about this, but you should know that
even a spent conviction needs to be declared in the application - this is one of the circumstances where you will need to declare the offence for all time, and an attempt to conceal it may also constitute an offence.
2, I have mental issue of depression and anxiety for many years, and I take medicine. I can provide my medical record and a letter saying I am on the waiting list to see a specialist. Can I request a warning letter or settle out of court because of my mental issue?
You can ask. If you are serious about this you need to engage a solicitor who will advocate on your behalf. Only you will know how your condition affects you, but you should know that TfL basically want to know that:
A) your disability or condition is so severe it contributed to your decision to commit the offences, so much so it would be totally unfair to prosecute you
and/or
B) your disability or condition is so severe that going to court would be in nobody's interest because of the extremely disproportionate effect a conviction would have on you
Some good examples that might qualify under A) are things like a severe learning disability, OCD, schizoaffective disorders with mania etc
Some good examples that might qualify under B) are things like a severe eating disorder, advanced cancer, chronic conditions etc.
But those are just off the top of my head and my own opinion, not from an official list - some conditions which might make it compelling that you should avoid the consequences of what you have done. I am not sure we have ever seen someone avoid prosecution because they have anxiety and depression, which, by way of perspective, is a condition that something like 10-15% of people in this country live with and manage.
That said, it may be worth consulting with a solicitor to explore your options. This will cost something like £500 to £1000 and there is no guarantee of success. A solicitor cannot invent mitigation for you, they can only advocate your position.