Mechanical Engineering

You'll need to qualify through JEE Main and JEE Advanced and you can get admission for first year of four year degree course. [Many state or private colleges will admin Diploma holder in second year directly, but not the IITs or NITs.]
Diploma holders are eligible to get direct admission in second year of B.Tech through different CETs of state governments.

For government UPSEE LEET colleges, your rank should be less than 50 and for private colleges, your rank should be less than 200.

Hello,
Here, I am suggesting you shiksha college predictor please visit:
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwiomMOV8ILcAhXFOI8KHdVpCDwQFjAAegQIAhAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H

Hello,
Here, I am suggesting you shiksha college predictor please visit on it
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwiomMOV8ILcAhXFOI8KHdVpCDwQFjAAegQIAhAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H.

Hello
Here I suggest you siksha college predictor please visit on it
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwiomMOV8ILcAhXFOI8KHdVpCDwQFjAAegQIAhAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H.

Yes, surely you can get a government engineering college in Uttarakhand with mechanical branch.

No, you can't get lateral entry in B.Com after Diploma. You can only get admission in B.Tech if you want to take admission via lateral entry.

The basic eligibility for admission to any of the B.Com. Programs is mentioned below. Candidates must pass in Higher Secondary School examination from a recognised educational board
They should have Maths and English as core subjects
Minimum 50% marks are required at 10+2 level
Although, candidates from Science and Arts stream are also eligible to apply, those with Commerce stream are preferred
There is no work experience required for the course. However, students with work experience can also apply.

To know about the fees please contact the college officials. For contact details visit:
http://www.cpclpolytechnic.com/index.php?page=contact

There is an official link of there placement records, take a look at it.
Link: https://www.iitr.ac.in/departments/ME/pages/Academics+Placement_Record.html.