Muktzeh and annulling practices at the husband’s instruction

Hi, I have a few questions:

1. Regarding muktzah on Shabbos. If there is a garment that is meant to be washed, for example it is lying on the floor, is it permitted to pick it up and put it into the laundry basket, or does it become muktzah?
2. I was used to certain minhagim, such as washing my hands six times when they were not clean. My husband told me that I may wash only once on each hand and that it is not necessary to wash six times. Do I have to listen to my husband? And in general, if the husband says that a certain change in minhag is permitted, is it allowed, or does it require hatarat nedarim?
3. In connection to the previous question. Usually I do not manage to daven the entire Shacharis because I work and I am also taking care of a small child. When I was a girl, I generally did daven everything. Does this also require hatarat nedarim?

Thank you very much!!

Shalom uVracha,

1. It is not muktzeh, since it is still fit for use.
2. In a matter that does not directly disturb your husband, you are permitted to continue with your minhag as you have done until now.

A practice that you thought was based on halacha, and you have now learned that there is no such halacha, does not require hatarat nedarim (annulment of vows).

3. You are exempt from prayer if you do not have time, and hatarat nedarim is not required.