Buying a new rear wheel
"700 x 38c - 28 "  You have a "700c" sized road tyre, in width of 38mm and the rim is 28 mm wide.  This tyre size is also known as 622-38 because it is 622 mm across.

A freewheel and freehub are the two different parts that do the same job.  Your bike might have either, but not both.  This is how the cogs in the middle of the rear wheel attach to the wheel's hub.

If you replace the rear wheel completely, you can reuse the tube and tyre.  You will need new rim (28mm wide) and rimtape.  New spokes, and a new hub.  If the cassette and chain are unworn you can transfer them over.
Your cassette is a "shimano branded CS-HG41 with 7 speeds" so its not the old-style freewheel


  For other readers, if the current hub were a freewheel (screws off) then replace it with a cassette that slides onto the hub and is held on with a lockring.  This will mean a new chain.  Freehubs are technically superior to Freewheels.


Your bike has 7 speeds in the rear, so either stick with that or if you want more gears then you'll also have to change the right-side shifter as well.  Don't feel compelled to upgrade the number of gears.