I am not in the UK Conservative Party but I actually know a few people who are and I hear enough of what going on in the party. I don't particularly like the conservative party however I signed up for account because of egregiously wrong you are.
a) Various leaders agreed to go on a show. Boris Johnson doesn't have to go on the BBC and the BBC can interview who they wish. Andrew Neil likes to make fools of people on his show. He has done it to many politicians of all colours. It is really just a higher brow version of "Ben Shapiro defeats Liberals with facts and logic". Jeremy Corbyn was stupid enough to go on there and get himself shafted by Neil.
b and c) Gove and Stanley Johnson was sent by their party to the debate. Channel 4 (which is mostly publicly funded which most people don't know) did the whole ice sculpture as a stunt. They already bought the sculpture. The
As for the BBC having a "right wing bias". Nothing can be further from the truth. You can go on the website yourself and there are thousands of stories talking about typically left wing talking points.
I am actually building daily news site analysis tool by cobbling together some sources. I am using some fairly simple word analysis techniques (most of the effort is scraping the data from these sites and deciding what constitutes a real news story) and most of the language on the BBC and the Guardian are similar. I suspect that most of them just copy and paste stories tbh.