My question involves real estate located in the State of: Texas

This boundary problem involves myself and two neighbors who I will refer to as Neighbor 1 and Neighbor 2.

My home was purchased by my parents and I 14 years ago from a lady who had owned it for 42 years prior to sale.

Neighbor 1's home is adjacent to mine and has been owned by him for 8 years. He rented it approximately 7 years prior to purchasing, and the house has been there for 25+ years.

Neighbor 2's home is adjacent to and on the opposite side of Neighbor 1. He has lived there for at least 14 years and I assume he owns the home. The home also looks like it has been there for 25+ years.

I want to maintain our current friendly relationship with Neighbor 1 but I do not know Neighbor 2 very well.
All three homes have "woven wire" fenced in back yards that have been there at least 14 years ( more likely 25+ years).

Apparently someone in the neighborhood has done a survey during the past year, and stakes were placed in the back alley approximately 2 ft. "off" our fence corners. Neither I or Neighbor 1 had noticed these stakes until this past week when Neighbor 2 announced that he was taking possesion of the 2 foot strip between him and Neighbor 1. He also sprayed some shrubbery and mowed the grass inside Neighbor 1's fenceline when no one was home. Now Neighbor 1 is all upset and wants to put up a privacy fence around his back yard. Naturally, he would like to put it 2 ft into my side of our current separating fence. This would be in line with the metal survey stake in the back alley. Actually, I wouldn't mind getting a new fence, but I have a 10 X 16 storage building up against the current fenceline, and there are trees and shrubs in the current fenceline.

Questions:

Do the survey stakes in the back alley really give us any reliable and or legal indication of where the property lines really are?
If the current fences really are off the property lines by 2 ft., isn't there some statute of limitations, etc. that come into play here?
How should I proceed?