M.S

Hi
P.HDS in USA and Canada are mostly funded in two ways. Either you receive a grant or you get graduate assistantship. The best way to apply in the University is to select the one which will have the course you are interested in. Write an email showing your interest to the concerned professor or department and then share your research proposal. You will get all info here.
https://www.findaphd.com/study-abroad/america/phd-study-in-usa.aspx

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Yes, you can. Your studies must be aligned with your career plans and you must know yourself why you want a MS now. Further you must take GRE and TOEFL for meeting the eligibility criteria. I will also suggest you email the universities before applying.

Keep in mind your career plans while choosing what to study as either one is good. In which field are you planning for MS?

Please specify the country in which you wish to pursue your Masters

In my opinion United States (US) will be a good choice for studying in MS. In US there are few good universities to pursue Engineering programmes like Florida International University, Stanford University, University of North Texas (UNT) etc.

At IITs and BITS you may be required to clear GATE examination or equivalent. Abroad, you will have to clear IELTS/TOEFL or GRE as required by the university of study with the required score to get admissions in a foreign university.

Hi , you are eligible for both , if you are interested for a managerial career opt MBA. On the other hand if you are keen for a career in research, academics and interested to work in the same field MS is the option. You need to decide basis your career goals at this stage for better prospects.
Hope it helps.