Why would you plead to something of you have no idea how it will affect you? Or even what it is?
Whether its a misdemeanor or felony depends on circumstances of the arrest. And yes, you do have to disclose a conviction. An expungement won't remove it from your record, but simply add a note indicating dismissal under Penal Code 1203.4.
These are all things you should have discussed with an attorney BEFORE you entered a plea.
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There are only a few things that make a DUI a felony. It doesn't sound as if your case involves any of them, and a refusal is not one of them. So, your DUI is almost assuredly a misdemeanor. In order to get it expunged pursuant to PC 1203.4, you first have to be off of probation, which is usually 3 years. If you are still on probation, and have completed all of your obligations, you may be eligible to have your probation terminated early, provided that enough time has passed. Hiring an attorney will make all of this much easier. Good luck.
Yes, you do have to answer yes to being convicted. Never plead to anything without fully understanding the consequences of your plea, especially with law school in your future. Assuming it is a misdemeanor, you can petition to have the conviction expunged after your probationary period is over. There are things you can do if it is a felony and/or you are still on probation, but you need to consult with an attorney.
These types of DUIs are typically treated as misdemeanors. If you are asked if you have been convicted of a misdemeanor, you would need to respond truthfully. For that reason, you should check your court documents and verify the level of offense (felony or misdemeanor).
While a felony or misdemeanor conviction can be "expunged" via Penal Code 1203.4, you will have some very serious issues to address with the bar. If you plan to practice law in California, the California State Bar may hold your moral character determination in abeyance for a few months or a few years. I have a client in this circumstance right now.
Ultimately, you should consult with a defense attorney to discuss your best options.