I would have thought myself that these were searches that could/should be carried out by a solicitor, but I'm no expert.
Re. (2) and (3), I would have thought that these are only likely to apply in a very small, and fairly obvious number of circumstances.
Re. (4)-have there been any extensions? Not all extensions actually require permission.
Re. (1)-What is in front of, beside and behind the property? Is it realistic that anything could be built in those locations?
That's only my own take-I'm as surprised as you are that a solicitor wouldn't undertake these searches, unless you have to specifically request them to do so.
There are a number of solicitors who contribute regularly to AAM, and hopefully they will clarify, or at least give their take on the situation.