There is no such thing as a Business Visa; there is either a short stay visa (type C) or a longer stay visa (type D).
- Can I make a trip to another Schengen country (not Sweden) from US without visiting Sweden at all.
Yes you can, however you will have to provide justification to the immigration agent for the purpose of your trip. For example, you may have to provide proof of a hotel reservation, of your travel itinerary, of sufficient funds to cover your trip, etc. Remember that a visa is not a guarantee of entry, it is simply a permit to request entry.
2) Can I make a leisure trip to another schengen country (not Sweden)
from Sweden after my business visit which is longer than my stay in
From this website we have the answer:
Your visa may only be valid for certain countries If you are granted a
visa you can also visit other Schengen countries.
In certain exceptional cases your visa may be valid for entries and
stays in Sweden or certain Schengen countries only, if you are
registered in SIS (Schengen Information System) or if your passport is
not accepted in all Schengen countries.
So if your visa states that it is valid for the Schengen states (and not just Sweden) then once you enter Sweden you are free to move about the Schengen zone without the need for additional visas.
The maximum stay allowed under the short stay (type C) visas is 90 days, but the actual duration of each visit will be written on your visa. It may state 90 days, or 30 days. This is how long you are authorized to stay in the zone.
Finally, unlike some other visas, the visa has to be valid for the entire duration of your stay. This means that if your visa expires in 10 days, you can only stay for 10 days. You cannot enter the day before the expiry and spend 9 days in the zone.