1. The best thing I've learned this year was something about myself.
2. The best thing I've learned this year is something about myself.
(Do we have to use 'was' or 'is' in the sentences? Are both OK? What is the difference between them? Can we use the past tense 'was' with 'have pp'?)
have learned Present perfect
Both are correct, as present perfect can denote actions up to the present, but completed, or denote actions up to and continuing to the present. Most usage is the latter usage, so 2 would be more common usage.
A}The best thing I have accomplished is running the 4 minute mile
B}The best thing I have accomplished was running the 4 minute mile.
The better usage is A, but B is acceptable. It really depends on does the writer intend for accomplishments to be continuing into the present, or not.