They have, from the accounts I’ve seen (including their own propaganda videos) a single flyable F-5 constituting their entire “fast air combat capability” of those delivered to Yemen more than 40 years ago (and the F-5 was an older cheap export fighter then.)
And... I wouldn't expect it to be flyable much longer. Mobile missile launchers may be hard to find and kill on the ground, boring conventional fixed-wing jet fighters aren't, and even though they aren't the strategic target of the coalition the US has put together, US combat doctrine very heavily favors early destruction of an enemy’s air combat capability and air defenses to maximize freedom of operation.
No. They couldn't. Yemen to either is like three times the range of the SU-22 on a shortest distance path, which would take them through Saudi Arabia and close enough for mistakes of intent to Israel, either of which—as well as Egypt—has Air Forces more than capable of intercepting and destroying them if they magically gained the range to try to pull of that kind of flight.
The Houthi Air Force is useful for their civil war, and not a whole lot else.
Their air force is a joke though. A single flying F-5 (vintage 1970), and some decrepit SU-22 Fitters with no range.
Also, those aren't "attack" helicopters. They're bog standard Mi-8 transport helicopters. You can use them to attack, but they're nothing like a Hind/Hokum/Havoc or Apache helicopter.
They have attack helicopters: https://pictures.reuters.com/CS.aspx?VP3=SearchResult&VBID=2..., https://pictures.reuters.com/CS.aspx?VP3=SearchResult&VBID=2...
They have American & Soviet fighter jets (F-5 / SU-22): https://pictures.reuters.com/CS.aspx?VP3=SearchResult&VBID=2..., https://lh6.googleusercontent.com/-H4BV3xzWWXk/TnIKIQMOAFI/A...
They have tons of cruise missiles: https://pictures.reuters.com/archive/YEMEN-SECURITY-PARADE-R..., https://pictures.reuters.com/archive/YEMEN-SECURITY-PARADE-R...
And ballistic missiles: https://pictures.reuters.com/archive/YEMEN-SECURITY-PARADE-R...
They're being supplied by Iran and whoever else hates Saudi Arabia, so they have a ton of capability to launch pretty devastating attacks on their neighbors -- hence why we have destroyers and aircraft carriers in the region. The missiles targeting merchant ships are bad -- it'd be worse if they started targeting land-based military targets in other countries.