Will previous fertility treatments increase my chances of getting pregnant again, without receiving new treatment?

No. Just undergoing previous treatments will not make it easier top become pregnant again. Becoming pregnant before may make it easier, but it really depends on the individual situation. It is always best to see a fertility specialist again to discuss things even if you do not do any treatment right away.
It depends. It really depends on what is the cause of infertility. The main causes of infertility are anatomic problems like blocked tubes, male factor (like low sperm count) or lack of ovulation. If the underlying problem has not been fixed then infertility treatment will likely still be needed.

Related Questions

Odds of getting pregnant past 35 with the use of any fertility treatments?

Depends. There is no way to answer this specifically for one patient. Overall pregnancy rates decline after 35 but most people can still get pregnant. Infertility treatments are highly successful. Next step is to schedule a visit with your obgyn to asses your needs and to put together a plan.
Generally very good. It can vary widely depending on your specifics, but overall female fertility up to the late 30's sometimes early 40's can be quite good.