Bought my 2001 V6 AWD Santa Fe last year used around 117k miles on it. Noticed a few problems, but have been trying to figure this out without spending too much.

When I start the engine it will rev at almost 3 revs for a little bit then gradually come down and rest below 1 rev after 10 mins. Also When I start driving, for the first 10 miles the revs will be above 2.5 revs then will come down to 2 revs when it "warms up". I noticed a difference in the summer with better revs. But the high revs at start up eat my gas and I notice a lower performance until it "warms up".

I have been told it might be a vacuum line problem and to check pvc valve. Also was wondering maybe if it might be a fuel pressure regulator problem. Any help would be a welcome.
Thank you!