Is it possible to pay the internal debt of the country and to cover the budget deficit by increasing taxes?
At the time of writing, the question is far too long.

From a simplified accounting perspective:

The government fiscal deficit = all expenditures - taxes.

The change in debt in a year is equal to the fiscal deficit (under simplifying assumptions).

So if the government can raise taxes without affecting anything else, the deficit becomes smaller, or turns into a surplus, in which case the debt falls.

The reason why this is not normally done is that raising taxes reduces growth. The exact effect of tax increases is an object of academic and political debate. If you search for “austerity policies” you ahould be able to find a lot of information.