Question

5. Extend your arms out to either side.
6. Lean forward, lifting one leg straight behind you.
7. Hold this pose, then return your leg to the ground and your arms to the sides.
8. Repeat with opposite leg.
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Are they grammatical? Don't we have to put 'the' before 'opposite'?

Answer 1

5. OK

6. OK

7. <i>Hold this pos<b>e; then</b> return your leg to the ground and your arms to the sides.</i>
[The word "then" is not a coordinating conjunction (one of the FANBOYS). It's a subordinating conjunction, and therefore needs different punctuation.]
http://www.chompchomp.com/terms/coordinatingconjunction.htm
Read the entire webpage to understand both coordinating and subordinating conjunctions.

8. Yes, this will read better if you put "the" in front of "opposite."

Answer 2

7. The semicolon is used in a compound sentence when no conjunction is used. The comma is appropriate when the conjunction is used to connect the sentences in a compound sentence.

Answer 3

I think we're splitting hairs here. "Then" may be used to begin a sentence. The semicolon is not incorrect here, but the comma may also be considered correct. I think no one, in this instance, is mistaken or wrong.