4432, 5332, and 4333 shapes are all balanced, and should be bid as such. It is my sense that these days, it is common to open 1NT even with a 5-card major, although it is not universal. Pairs with weak 1NT openers are less likely to open a 5-card major with 1NT because they have a different set of methods than pairs with strong NT openers.
In America these days, a "strong no trump" implies a 15-17 HCP range for 1NT openers, so you'd open a 4432 like so:
- With 12-14 HCP, open a minor and plan to rebid 1NT.
- With 15-17 HCP, open 1NT.
- With 18-19 HCP, open a minor and plan to jump to 2NT.
- With 20-21 HCP, open 2NT.
4441 is the hardest shape to bid, since systems are mostly not built with them in mind. My preference is to open the lowest 4-card suit. With 16+ (not counting any singleton honor), you can splinter if partner bids one of your suits. If your short suit is spades or clubs, you can rebid 2H (slightly lying about your shape) when partner bids your singleton. If your short suit is diamonds or hearts, with 17-19 you'll have to rebid 2NT, and with 20-22 you'll have to jump to 2S when partner bids your singleton.