For an unvented cathedral ceiling, the only effective choice is spray foam or extruded polystyrene above the roof decking. Dense-packing an unvented cathedral ceiling is asking for certain trouble.

HE said they could spray the walls but not the ceilings or attic.

That's ridiculous. Unless, of course, you've already dry-walled the ceilings.

The basement is part of the conditioned space of the home; there's no point or need in adding insulation, other than for sound attentuation.

An ERV or HRV is a good idea in a heating climate such as yours.

All these decisions should have been made in the design process in consultation with your architect or designer.

there's no point or need in adding insulation on the basement ceiling.

Touching on your other questions- An HRV would be ideal for your climate. Any time a home is tighter, you need to have mechanical ventilation installed. They are not terribly expensive, and run between 1-3k depending on the size required and if you go with dedicated ducting (more efficient).
A blower door test is a good idea to confirm air sealing and tighness of the home. Anything below 3 air changes is a good starting point, but less is much better. They are typically not very expensive, around here they cost around $300-500. That money is well worth it assuming they will find leaky areas in the house that will rob your heating and cooling for years to come. Air sealing is more important then insulation, as insulation (with exception of spray foams) does not air seal. Caulking is much cheaper then spray foams.

Fine Housebuilding had a good summary article a few moths ago.

The foam can provide excellent air sealing, while using batt to raise the overall rating is often cost effective over a full foam job.

Part of the 'trick' is to make sure the frost point stays withing the foam layer.