Is it okay to say "I PAY ATTENTION TO the house" in the sense I watch it or look after it? Because I am afraid it is a lexical misuse
Idiomatically, to pay attention to the house would mean to watch it carefully - as in literally keep an eye on it. For example, if someone was trying to get you to notice some subtle pattern in the way lights changed on a house, they might tell you to pay attention to it. If you were watching a video where something interesting happened to a house in the background, while your attention is normally drawn to something in the foreground, someone might tell you to pay attention to the house.
On the other hand, to watch the house could mean that, or it could mean a more figurative sense, as could keep an eye on the house. In those cases, it might mean making sure that nothing has happened to the house, letting someone know if it gets burgled, and if it's over a longer period of time probably going in every so often to air it out and make sure there's no damp or mould appearing. I wouldn't expect someone to use pay attention to the house to give those meanings.
To give attention to the house wouldn't be a commonly used phrase, but it would, I think, be understood to mean actively doing things to keep it in a good condition, as would maintain the house. Give attention could also be used to mean actively upgrading the house, but I wouldn't encourage anyone to use it for anything. Maintain, on the other hand, is a completely natural and commonly used term.