In English we take permission by asking “May I come in”, “May I use this”?

In Gujarati, we can create such requests by using the sentence in simple present tense or sentence with “to can” and just omitting form of હોવું(hovuM) and asking it in question tone

I come -> હું આવું છું (huM AvuM ChuM )
I can come -> હું આવી શકું છું (huM AvI shakuM ChuM)
So ,
May I come ?-> હું આવું ?(huM AvuM) OR હું આવી શકું ? (huM AvI shakuM )
I go -> હું જઉં છું (huM ja uM ChuM )
I can go -> હું જઈ શકું છું ( huM jaI shakuM ChuM)

So,
May I go ?-> હું જઉં ?(huM jauM) OR હું જઈ શકું (huM jaI shakuM ?)
I do -> હું કરું છું ( huM karuM ChuM )
I can do -> હું કરી શકું છું ( huM karI shakuM ChuM )

so,
May I do ?-> હું કરું ? ( huM karuM ?) or હું કરી શકું (huM karI shakuM ?)

We can omit “હું”(huM)

We come -> અમે આવીએ છીએ(ame AvIe ChIe )
We can come -> અમે આવી શકીએ છીએ (ame AvI shakIe ChIe )
So ,
May we come ?-> અમે આવીએ ? (ame AvIe ?) OR અમે આવી શકીએ ? (ame AvI shakIe ?)

We go -> અમે જઈએ છીએ(ame jaIe ChIe )
We can go -> અમે જઈ શકીએ છીએ (ame jaI shakIe ChIe )
So,
May we go ?-> અમે જઈએ ? (ame jaIe ? ) OR અમે જઈ શકીએ ? (ame jaI shakIe ? )

We do -> અમે કરીએ છીએ(ame karIe ChIe )
We can do -> અમે કરી શકીએ છીએ(ame karI shakIe ChIe )
so,
May we do ?-> અમે કરીએ ? (ame karIe?) or અમે કરી શકીએ ?(ame karI shakIe ? )

Please refer this lesson to form sentences with verb “can”
Using verb “Can/To be able to” in Gujarati

In English, we request others by asking question,
“can you please give your pen ?”, “can you please open door ?”.
In Gujarati also we request same way, but generally, such questions are asked in the future tense as if asking “will you be able to give your pen? “, “will you be able to open the door ?” etc.
You can form such questions using the above mentioned lesson.

But there is another way of asking such questions to request others. In Gujarati such questions can be asked as if “will you give your pen”, “will you open the door”
e.g.
can you please give your pen -> will you give your pen ->તમારું પેન આપશો ?(tamAruM pen Apasho ?)

can you please open door -> will you open the door -> બારણું ઉઘાડશો ? (bAraNuM ughADasho ?)

Sometimes such sentences are started with words like જરા (jarA) to sound it more polite.
e.g.
જરા તમારું પેન આપશો ?(jarA tamAruM pen Apasho ?)
જરા બારણું ઉઘાડશો ? (jarA bAraNuM ughADasho ?)