"exerts and responds to forces to/from their surrounding"": how to revise?

The only way I can think of is

It exerts forces to and responds to forces from their surrounding

But I am only risking it in fact. A native speaker might be able to tell us if "acrobacies" of such kind are acceptable.

You can certainly try and find synonyms of forces so as not to stumble on its repetition:

It exerts forces to and responds to impacts from their surrounding

Note: I have respected the precise context you have given but actually the more idiomatic phrase is

to exert force(s) (singular is more common) on something

As commented earlier, an appropriate word is interaction.

The key to this is the prefix inter:

inter = a prefix occurring in loanwords from Latin, where it meant “between,” “among,” “in the midst of,” “mutually,” “reciprocally,” “together,” “during” (intercept; interest); on this model, used in the formation of compound words (intercom; interdepartmental).

Dictionary.com

I emphasize the mention of reciprocity, that is of reciprocal action. An interaction therefore cannot be one way. It necessarily involves action of one on the other, and vice versa.

From this perspective I argue that if "It" (whatever it may be) interacts with its surroundings, each affects the other. "It" exerts a force on the surroundings and they exert a force on "it". In classical physics this is a trivial statement consistent with one of Newton's laws. If the force is more metaphorical than in physics the mutuality is still interactive.

"It interacts with its surroundings." says what needs to be said.

I'm not sure what it and their refer to, but I think you might need to make them agree—either it/its or they/their. As for the compact wording, try:

[...] such as how it responds to and exerts forces in its surroundings

[...] such as how they respond to and exert forces in their surroundings

To expand it back out:

[...] such as how it responds to forces in its surroundings and exerts forces in its surroundings