FOR DENISE CANN ONLY, I understand, at a given time only one status can be used to enter in USA and to maintain legal

:-) Hi! Let me read your questions.

Q1) Can I hold different types of visas (H1B, H4, L1B, B1/B2 etc.) at the same time and enter in USA depending on the purpose of my travel (e.g. H1B for business travel or H4 for family travel)?

If you enter on H4, you are not authorized to work. So, if you are in the US for 3 months, you are NOT permitted to work. If you enter on an H-1B visa, then you are authorized to work for the company that petitioned for you for which you have approval.

Q2) If yes, then can I go for stamping H4 first, then after few days go for H1B visa or vice-versa?

Technically, you may do so although you may draw questions from the consular officer.

Q3) Can I fill two DS160 at the same time and schedule two visa (e.g. H1B as well as H4) interviews having 1-2 weeks gap in-between? Or, do I have to provide any information in the 2nd DS160 about previous/most recent visa?

To be safe, work with one first and proceed from there.

Q4) While issuing the second visa, does US Consulate cancel or invalidate previous visa?

They may.

Q5) I mean, by law can someone legally hold different visa types simultaneously for the same country and use it interchangeably in the future depending on the purpose of their visit or entry (e.g. H1B for business travel or H4 for family travel)?

H1B is very particular for the purpose of being employed by the petitioner that petitioned for you. Each time you leave and re-enter, you have to prove that you have continued to maintained that status including pay stubs, etc. In this day and age, I would stick with one and commit to it unless you have lost your employment and needing H4.

You are permitted to have two visa stamps with unexpired visa validity dates. The visa that you choose to enter the US will be the status you are in. I would caution doing this frequently, especially regarding the H-1B visa.

Also, I would make sure that your I-94 reflects the status that you intend.

You are very welcome! Have a wonderful evening. :-)

Also as an aside, the H4 will only be valid so long as your wife maintains her H1B status.

You're welcome. Please check other thread.