Question on huf

- Does the HUF automatically transition to Elder son ?

Yes, but only as KARTA

or we need to do something here ? ........ Inform the same to related parties.

- How do we determine who were members of HUF and who were coparcener's when it was formed or

By default everyone in family is either member/coparcener as existed before.

- Can the younger son demand separation of HUF and in that case how will the assets / money of the HUF is handled?
Any Coparcener can demand for dissolution of HUF and as such equal partition of the property/assets.

- Does this mean that the money loaned by HUF has equal right of all coparcener and members in equal share?
YES

Can Mother become the Karta of HUF as father named her on everything in the Will.

No.... Not in this case.

There are two copercener (sons) and 1 member (mother) left after father passed away. 

That's wrong. The family members of the brothers are also to be included.

- One of the son's wants to divide the HUF ? If that happens; will it become Two HUF of same names?
Father's HUF gets dissolved, the receipts can be inherited by sons' HUFs.

- Are the wifes and children of the the copercener also considered members ? 

Yes, children as coparceners & wives as member

If they decide to dissolve the HUF 

- Will the loan be now equally divided between all copercener and members ?

YES

- If Yes, how will that now be reflected on the balance sheet of company; as a loan for each of these individuals ?

The amount is first transferred to original HUF account. After dissolution of it new members or HUF may give loan afresh.