Pammi would you like to eat food with me... is this past? Isn't it present?

4) would like;-- its used for wish, modified form of want Ex;-- i wud like to take part in competition. I wud like to ask a question. I wud like to speak english fluently. So i think here in ur sentense u r showing ur wish with politeness for future proability..

1) if there is a joint sentences and first part is in past tense so in 2nd part we use would in place of will. Ex :- he said, he wud help us. I knew he wud win. I knew that he wud not get thst job. I had no doubt that u wud win.

2) for more politeness use would in place of will. Ex:-- wud u close the door as u go out? Wud u help me to fold up the bed sheet.

Sumtimes it is used in place of will also.. Ex you would not believe this but its true.

its not past. its one kind of future, but showing probability not surity.

"Will" suggest strong probabillity or future likelihood. "Would" impiles the same but used when probability is more hypothetical. Would has lots of meaning.