1. We have three PE classes a week.
2. We have three P.E. classes a week.
3. We have three pe classes a week.
4. We have three p.e. classes a week.
5. We have three Physical Education classes a week.
6. We have three physical education classes a week.
[Can we use all the expressions? Which ones are unacceptable?]
1.We have three PE classes a week.
8. Thee are three PE classes a week at/in school.
[Does #1 mean #8? Can we use both 'at' and 'in'? Are they the same in meaning?]
If Physical Education is the formal name of the class, then 1, 2, and 5 are correct. However, if you're referring to physical education in general, and the actual classes have distinct names (Girls Physical Education 9, for example, or Boys Soccer 11), then 1, 2, and 6 are correct.
If you mean "There" at the beginning of 8, then yes, 1 and 8 have the same meaning. Either "at" or "in" are fine.
In terms of acceptability, all six expressions are grammatically correct and can be used interchangeably to convey the same meaning. The choice of using "PE" or "P.E." is a matter of personal preference or style, as they both represent the acronym for "Physical Education." Whether you capitalize all the letters ("PE") or use periods ("P.E.") is not particularly significant, as long as you are consistent throughout your writing.
Regarding your second question, the sentence #1 "We have three PE classes a week" does convey the same meaning as #8 "There are three PE classes a week at/in school." The prepositions "at" and "in" can both be used in this context, but they provide slightly different nuances.
Using "at" implies that you are specifying the location where these PE classes take place. For example, if you say "There are three PE classes a week at school," you are emphasizing that these classes occur specifically within the school premises.
On the other hand, using "in" indicates that you are referring to the broader concept or institution of school. So, if you say "There are three PE classes a week in school," you are referring to the general practice of having PE classes as part of the school curriculum.
Both expressions are acceptable, and the choice between "at" and "in" depends on the emphasis you want to convey.