Signal
 

NFHS rules.
1. What is the correct signal if a player touches the ball a second time and it is also the teams 4th touch.
2. Correct signal if on the teams 3rd touch a player hits the ball into the net and the same player catches the ball as it comes out of the net.

I only use NCAA-W, but I can tell you what I was told and why, and then you can decide if it's worth listening to. :)

I was told that if you have a choice of a team fault or an individual fault, give it to the team. So if a player's second contact is also the team's fourth contact, I would indicate 4 hits.

In your example of a player catching the ball out of the net, I would again call 4 contacts.

I believe Scrapper is right. Both NCAA and NFHS say the 4th contact by the same person should be ruled as 4 contacts. USAV, on the other hand, states it should be ruled as a "2 hits" violation if the contact is made by the same person.

The 4 hit signal has been explained to me this way:

If anyone else had hit it, it would still be illegal. That is why it it is 4 hits, not the double/ illegal hit signal. If someone else had doubled on the next hit, it is not illegal from that, it is illegal from the touch.

Caveat on the NFHS interpretation. If the 3rd contact is a double contact (as opposed to successive contacts) which would be signalled with two fingers if it were the second contact, the signal would be "two" and not "four."