Ulpan is a class that is free for a Jewish immigrant to Israel. I am wondering whether it is open to non-immigrants and if so, at what cost? (Assuming the prospective student can legally stay that long.)
A visa type A/2 is for students taking classes but I do not know whether ulpanim are included.
Ulpanim are usually sponsored by the government or the Jewish Agency. They're free to olim because someone else pays.
Most of the ulpanim require signing up through the immigration office which you won't be able to do. There are some open to the general public, however, where you can pay on your own.
Quick Google search shows some private options (example, not affiliated), and universities also offer it to foreign students (example 1, example 2[he]).
As to visa type - inquire with the consulate. For A/2 I believe you have to be enrolled into accredited institution, I don't know if ulpan counts.
I have personal (although long-ago) experience with Hebrew University’s ulpan and recommend it highly.
I was a non-immigrant foreigner… it's a money-maker for the University. The Summer Program is open to all. The web site now seems to make it look like the regular semester programs are open only to students and several other categories. That was not enforced back in 1998. Can't speak to today.
