Where can I get fresh limes? If not, lime juice?
Try fruit store around the corner from Bar ilan and Shmuel Hanvi in closer to Bucharim.
The store has an Agudah hechsher. I can try to get the exact location soon.
Is that just any fruit store or you actually think they might have limes cuz I went to Machane yehuda fruit stores, osher ad, sharei revacha ect..and they didn’t have
it has a pretty big selection at times when no one else had, they had, I don't use them since I dont use Agudah also in Israel things are seasonal.
No, I do not know for a fact.
Lime is seasonal and even then hard to get. Late July until late September. Pomerantz make frozen juice you can buy. When is season they easiest to get is those distributed by חוות תקוע.
Remember, It's shmita! everything may be harder to find, especialy with a decent hechsher.
At this point basicly all fresh fruits (unless imported or some apples) are
Otzar Beis Din and have Kedushas Shvieis with the relevant halachos of what you may (or may not) do with them. Before you do the effort to find the limes, find out if what you want them for is a permitted use...