Arena Animation, FC Road

Technically, you can do a Masters if you have Bachelors. But, when you apply for a Masters in fashion design the requirements are to submit a portfolio. These portfolios are really elaborate. For example 12 garments designed and sewn by you. Fit on a model with pictures taken, etc. Also, there might be a design challenge. So, if you have your portfolio you can surely apply for M.Des.

Follow the link given below to get a clear comparison between the 2 institutes:
https://www.shiksha.com/resources/college-comparison-119219-108037

Yes, you can do it either in the morning or evening batch.
By the way, the course have been revised and upgraded as Animation Prime.

I am not really sure if they allow such transfer from one location to another. Request you contact your branch for the same and understand with them the procedure of transfer.