1. how did the romans respond when they saw the way the british soldiers fought?

Initially they were cautious and defensive; Caesar's first invasion got bottled up at the coast, and withdrew. His second fared better, and it became clear the Britons could not defeat Caesar in a pitched battle. They turned to guerilla warfare, using chariots for mobility, and slowed the Romans down. The Romans used their close infantry tactics to punch through British positions, such as fortified fords, and built camps for defence. These tactics paid off, and Caesar was able to set up the Trinovantes as a tributary nation. 

The subsequent invasions followed similar methods. The Roman advantage of armour and close infantry tactics usually paid off, and they were able to choose which tribes to make an example of. Mostly the rest would surrender. This became harder, though, in the mountains of Wales and Scotland; the local tribes used ambushes and guerilla warfare to their advantage. The Romans went about destroying their settlements, trying to bring them to heel. 

England and Wales was eventually subjugated, but much of Scotland was not. The Antonine wall between the Forth and Clyde marked the northern frontier.