Could there be a chance that I could go pay my boyfriend’s ticket about 4 years ago for driving without a license for him?

If it is actually a ticket for an infraction, and has not gone to warrant, yes, it can simply be paid at the clerk's office. If instead, there is a warrant, you must turn yourself in to the issuing court, with or without an attorney. On felony charges, the defendant must be personally present at every court hearing and appearance. On misdemeanors and infractions, an attorney can appear in court without the defendant being present which is safer and avoids immediately being taken into custody. You'll try to negotiate a recall of the warrant[s] and seek bail reduction or OR release. You'll try to negotiate a plea bargain on any Failure to Appear charge or probation violation that caused the warrant. You'll try to negotiate a plea bargain or take to trial the outstanding charge that caused the warrant. Effective plea-bargaining by your attorney, using whatever legal defenses, facts and sympathies there may be, could possibly keep you out of jail/prison, or at least dramatically reduce it. Unless you're competent to effectively represent yourself in court against a professional prosecutor trying to put you in jail, most people hire an attorney who can. If serious about hiring counsel to help in this, feel free to contact me. Conviction of any misdemeanor or felony crime is grounds for deportation, and the courts may report the conviction to INS.

I am not sure about your question. If he only has a fine which is due anyone can pay that fine. If he has never appeared then there could be an issue. There may be a warrant, he could probably post bail. If he posts bail, it is unlikely that ICE will be notified, but it is possible . If you can you should get an attorney and the attorney could appear for him and probably get his warrant withdrawn, but he may still be required to be booked, have his prints and picture taken. There is no guarantee that he will not be picked up by ICE, but some may even depend on his circumstances and he may qualify to get on the path to citizenship but that has not been passed by Congress or signed by the President.

Of course you can pay the ticket; anybody can pay the fine, the government just wants the money. But you might consider consulting with a good immigration lawyer about the immigration issues. It might be well worth the time and expense to avoid real problems in the future.