can liquid repair void warranty and applecare

The warranty was voided by the original liquid damage. Having it worked on by an unauthorized 3rd party will forfeit all rights to out of warranty service or replacement from Apple.

It really depends. Apple generally considers liquid damage to render the device ineligible for service. There are variations on third party service before a warranty expires - most notably because of the Magnuson-Moss Warranty Improvement Act in the United States. That states that a warranty or extended warranty can't be denied because a user of a product chose third party repair or service, and I've certainly heard of Apple treating that differently than servicing after the warranty has expired.

If you had been around 5 years ago you could have participated in this discussion back then. That is a misinterpretation of the Act and to how it works with the iPhone. Service managers at Apple Stores have some leeway in working on iPhones brought to them that have been worked on by non-AASP 3rd party sites. I always state that Apple may refuse to work on an iPhone that was worked on by a 3rd party site. As to liquid damage it will depend on how far the 3rd party had to go in bringing the iPhone back to life. If they had to replace the battery then the manager can authorize work on the phone in the OP agrees to have them replace the battery. If the 3rd party had to replace the power IC on the logic board they will generally refuse to do anything with the device. There were times in the past when they would allow an out-of-warranty replacement of the device but after Angela Ahrendts took over this latitude was greatly reduced.