ZackSaavedra

You're very welcome, Beverly. Better not mess with these, because they're actually wasps with excruciating stings.

Looks to be a Philodromid crab spider, pamsai. I only deal with US genera though, so I can't narrow down the ID any further.

No way to tell what genus of lycosid this is, as the spiderlings are obscuring the pattern on her abdomen. I'm not saying that's a dead giveaway, but it's helpful in most cases. It's a wonderful sight nonetheless.

This is a juvenile female, as they take some time to mature.

All I can tell you is that it's a Thomisid crab spider. I can't see any defining features in the angles you took, unfortunately.

This species is no longer placed in Achaearanea. Parasteatoda is the correct genus now.

Coupled with the body shape, I'd say it's certainly a Philodromid.

However, I'm not someone who can go any deeper than family level. We're talking Romanian spiders here. I haven't got a clue, ha ha.

This is not Z. sexpunctatus, this is Hentzia palmarum.

It'd be great if you could replace the current scientific name with the correct one, Caris.

Eye arrangement strongly suggests that this is a Philodromid crab spider. I can't say for certain though. I'm not a Romanian spider junkie!

Lycosoidea is a superfamily containing many families, including Lycosidae. I assume that's what you meant?

Ah, I see. It looks very similar to Allocyclosa bifurca, but New York is not part of its range. Since you said the abdomen was round and smooth, that also rules it out. Oh well, better luck next time huh?

If you find another spider, try to get photos from multiple angles, i.e. from above, from the front and rear, and from below if possible.