Both are correct but mean different things. Blessed by means that your people bless you, presumably because of your service to them, your example to them or your accomplishments. Blessed with means that it is a blessing to have the people that you have. It could also means that you are being blessed at the same time as your people.

It depends on what you mean. I think what you are trying to express is that "my people are a blessing to me". Which is an ongoing action or trait of your people. Both phrases you listed express the idea of something being done in a specific moment like at a religious ceremony or other public event.