Both words refer to growing or becoming greater. To increase is to grow in number, size, strength, or quality. It implies the simple fact of something becoming greater as opposed to shrinking or staying the same: The population increased by 2 percent. Escalate, which derives from escalator, an invention in use by the 1920s, suggests a steeper, sometimes alarming increase in intensity or magnitude, sometimes in prices, but more often in tense situations. If a situation, confrontation, or conflict escalates, it begins to get out of hand or threatens to escalate into something full-blown.
Climb covers all means of physically going up or reaching the top of something using one’s hands or feet or both—climbing a rope, a mountain, or the stairs. Clamber suggests a difficult or awkward climb that requires the use of both hands and feet: clambered up the rockface, the ladder, or aboard the ship. In actual usage, clamber is sometimes used for a more crawl-like action: clambered along a 40-foot log; clambering among the ruins. And to say that climbing plants clamber up walls (using their tendrils) is also an acceptable use.
Both adjectives can be used to describe when a person is unsure or doubtful about something. Someone who looks uncertain or who is uncertain what to do, think, or choose simply may not know what to do or think, out of lack of confidence. Ambivalent suggests having two conflicting or opposing feelings simultaneously, and for this reason being undecided: I’m ambivalent about the movie. There is a tendency to use ambivalent in contrast to affirmative or positive, so it seems to suggest a degree of negativity towards something based on a lack of decisive sentiment: You seem ambivalent about going out with her.