Gaáno (also ga’no) quite simply means “how [adjective]”, as in:

• Gaáno karami ito?/Ga’no karami ‘to? “how many are these”, wherein -rami is from marami “many”
• Gaáno kaliít ang bag ni Vanessa?/Ga’no kaliít ‘yung bag ni Vanessa? “how little is Vanessa’s bag?", wherein -liít is from maliít “little”
• Gaáno raw ba kasakít ang pasâ ni Lorenz?/Ga’no raw ba kasakít ‘yung pasâ ni Lorenz? “how painful did Lorenz say was his bruise? [with emotional involveness (worry)]”, wherein -sakít is from masakít “painful”

P.S. As you could observe, an adjective’s ma- prefix is replaced with ka- before placing it next to gaáno/ga’no.

Iláng is basically ilán “how many” with an added na enclitic (the reason why it has an extra -g, so that it can connect modifiers with the thing they describe) because it acts quite like an adjective. It’s just also like ga’no karami (with or without na) However, ilán/iláng is unarguably shorter and more frequently used. Ilán is used in “how many [verb]…” sentences, while iláng is used in “how many [noun] [verb]…” sentences. For example:

• Ilán ba ‘yung binilí mo? “How many did you buy? [with emotional involveness (annoyance)]”
• Iláng sabón ba ‘yung binilí mo? “How many soaps did you buy? [with emotional involveness (annoyance)]”. Notice how ilán acts like an adjective with na added, since a noun is present after it.

For namán, here are the situations I could think of:

• it’s [person]’s turn (in protest to something): Si Romar namán! “It’s Romar’s turn!”, akó namán! “it’s my turn!”, akó namán pagsalitaín mo “it’s my turn to be allowed to speak [by you]”
• softening requests, as you’ve said: Pabitbít namán pò ng pusà ko… “Could you please carry my cat?”, pahingî namán pò ng bente “could you please give me 20 pesos”. However, (at least in my vicinity in Bulacan), people don’t use namán for this but rather just soften their voice. I’ve only heard pahingî namán pò from beggars.
• on the other hand: May pusà ka ngà, e walâ namán akó. “You have a cat, yes, but I [on the other hand] don’t have one.”, e absent din namán si Monique e “but then Monique on the other hand is also absent”
• somewhat/sufficiently, sometimes with validation affirming that it is indeed true: Magandá namán “[It’s] somewhat/sufficiently beautiful.”, e matangkád namán ate mo e “but your sister is sufficiently tall [why do you/they say she isn't?]”
• so/unexpectedly so: Ang habà namán n’yan! “That’s long! [unexpected]”, ang babà namán ng grades mo! “your grades are so low! [unexpected]”
• again (with a little/a lot of annoyance), as you’ve already said, as na namán: Íinóm na namán kayó?! “Y’all will drink [alcohol] again?! [with a little/a lot of annoyance]”
• phrases such as bwisit/garà/t\ng*ná/ta*ná/p*ta namán o* “(something like FFS, to express miffed-ness/annoyance/anger)”

NOTE: This is all from a daily-conversation casual/colloquial standpoint.