The analyses of a text #1

The protagonist, Philip, who was born with a club foot, moved in with his uncle Mr. Carey after his mother's death.
He stays at a boarding school.
The following is the explanation about King's School at Tercanbury.
Chapter nominated Tom Perkins, the son of Perkins the linendraper as a successor of Dr. Fleming, the headmaster of King's School at Tercanbury.
Here "they" refers to the masters of King's School at Tercanbury.
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They all knew Tom Perkins. The first thing about him was that he was not a gentleman. They remembered him quite well. He was a small, dark boy, with untidy black hair and large eyes. He looked like a gipsy. He had come to the school as a day-boy, with the best scholarship on their endowment, so that his education had cost him nothing. Of course he was brilliant. At every Speech-Day he was loaded with prizes. He was their show-boy, and they now bitterly their fear that he would try to get some scholarship at one of the larger public schools and so pass out of their hands. Dr. Fleming had gone to the linendraper his father--they all the shop, Perkins and Cooper, in St. Catherine's Street--and said he hoped Tom would remain with them till he went to Oxford. The school was Perkins and Cooper's best customer, and Mr. Perkins was only too glad to give the required assurance. Tom Perkins continued to triumph, he was the finest classical scholar that Dr. Fleming , and on leaving the school took with him the most valuable scholarship they had to offer. He got another at Magdalen and settled down to a brilliant career at the University.
[Of Human Bondage by Somerset Maugham]
1. I'd like to know what "Mr. Perkins was only too glad to give the required assurance" means.
2. I'd like to know why it is "continued to triumph," not "continued triumph."
3. I'd like to know if "had to offer" means "were able to offer."
Thank you in advance for your help.