Right issue and its impact on existing share holder

Price will be according to demand & supply and other factors. Currently there is Urja Global Rights Issue going on, you can add URJA-RE to your watchlist and check the price to get an idea.

You can sell the Rights Entitlement just like you sell stocks, though you can sell them only in specific time period.

You can check out this post for more information: Everything You Need to Know About Urja Global Rights Issue

If one doesn’t sell Rights Entitlement, and doesn’t apply for rights shares then likely yes.