1) If my carry on is overweight I tell them to shut up and go away. Normally works
2) I think it is potentially a bit tight at LIM but you are presumably the whole itinerary on the same ticket so not to worry
3) Ecuador no yellow fever required, are you specifically referring to GPS? If you have heard that yellow fever cert is required then why not just get the yellow fever jab rather than risk a) getting yellow fever and b) passing it on to someone else? It's the sensible and responsible thing to do.
4) a. LAX LIM - LP long haul food, will be beef or pasta or beef or chicken with beer or wine
b. LIM CUZ LIM LP domestic packet of snacks with beer after 10am
c. LIM GYE LP regional international snack service which will be a horrible small ham and cheese croissant plus a chocotejo and beverage service.
d. GYE GPS. Don't know
e. GPS GYE See d
f. GYE LIM see c
g. LIM LAX see a
5. Yes LAN Peru will not give you alcohol for breakfast
Edit: LAX LIM LAX might be operated by LA not LP, same but nicer food in my opinion.