A basically new black garment cannot be shaken out if it is wet if the person is careful to have it cleaned.

If the garment got dirty with dust, it is preferable to also not shake it out.

Chapter 302 Section 2

‘Makeh bipatish’ is the melacha of finishing a product.

Strings that are left at the end of making a wool garment is prohibited because of makeh bipatish, if the person is careful about not having it. If he is not careful then it only prohibited rabbinically.

Chapter 302 Section 3

You are not allowed to fold clothes on Shabbos on its crease unless it is colored, white, new, he wants to wear it later that day, he has no other and you are folding it by yourself.

You can make your bed on Shabbos, if you will use it later that day. However if you will not be using the bed on Shabbos it is prohibited, unless you are using the room on Shabbos and it makes the room look very messy.