I sometimes get confused between “pelo menos” and “ao menos” so here are some jottings about different expressions with preposition+menos. They can just occur randomly. For example “A simplificação traduzir-se-á, no entanto, por menos exigências administrativas” just means it’ll result in fewer administrative overheads, but this is about where they’re used together with more co-ordination. The bulk of it comes from Ciberdúvidas and from Gramática Aplicada Níveis B2, C1.
Pelo menos means “at least” and can be used anywhere you’d use “at least” in english including seemingly idiomatic things like “At least tell me your name, even if you won’t tell me anything else”
Is essentially the same as pelo menios but with the important difference that you can’t use it for quantity – so if you’re saying “I need at least ten chickens” it’s “preciso de pelo menos dez frangos” and not “ao menos”.
A menos que
This means “unless” and since it introduces something that only might happen, it needs a subjunctive:
“Eu estarei lá a menos que chuva” (“I’ll be there unless it rains”)
Por menos …. que
There’s a set of phrases in Gramática Aplicada that correspond to english phrases like “No matter how much money you have, you can’t buy happines”. There aren’t any examples that use “menos” but on the same principle I assume you can do this sort of thing:
“Por menos roupas que eu use, estou sempre som suor” (“no matter how little I’m wearing, I’m always sweaty”)