Q.1: How does Jekyll describe Lanyon? What does it suggest about Jekyll's feelings about his own abilities?
Jekyll describes Lanyon just after Utterson mentions Jekyll's will. He compares Utterson's 'distressed' attitude about the will with Lanyon's about his scientific work.
Jekyll also calls him a 'hide-bound pedant', which has obviously a negative meaning. Then, he shows disagreement for a scientific matter. He says: 'what he called my scientific heresies'. It means that Jekyll and Lanyon don’t share the same opinion; Jekyll doesn't believe his own ideas are heresies. By saying that Lanyon is 'an ignorant blatant' and that he was disappointing, Jekyll means that Lanyon has an out-dated vision of science, whereas he claims his new concept is right and that Lanyon ought to be less narrow-minded.
However, Jekyll keeps saying that Lanyon is 'a good fellow […] an excellent fellow' and he wouldn't refuse to meet him again.
Q.2: What does Jekyll ask of Utterson at the end of the chapter? Why does Utterson have strong misgivings about this request?
At the end of the chapter 3, Jekyll wants Utterson to promise that he will 'bear with him [Hyde] and get his rights for him'. Utterson would like Jekyll to say the truth about this whole story. He worries about his friend; because it's written in his will that if he disappeared for more than three months, Hyde would inherit his possessions. But Jekyll answers his friend what he believes is wrong: 'it isn't what you fancy'. He adds he 'can be rid of Mr Hyde'.
Even though, Jekyll has strong misgivings about this request, because he has heard something 'abominable' about Hyde and he assumes that he can't pretend he shall ever like him'. Previously, he had learned that Hyde had run into a little girl (see Chapter 1). Moreover, when Utterson had spoken with Hyde (see Chapter 2), this latter was rude to Utterson. Additionally, he is ugly and it's believed that a