MAKE EACH OF THE FOLLOWING STATEMENTS PARTIALLY NEGATIVE BY USING PARTIALLY NEGATIVE VERB. FOR WHICH CAN THE ADVERB BE PLACED IN FRONT OF THE SUBJECT?

I am confused for which the adverb can be placed in front of the subject and which is correct in the following:

Marie studies with Ken.
-Seldom does Marie study with Ken. (or is it: Marie seldom studies with Ken.)

The farmers were able to support their families.
-Just barely were the farmers able to support their families. (or is it: The farmers were barely able to support their families.)

The patient could speak.
-Hardly could the patient speak. (or is it: The patient could hardly speak.)

The tenants complained to the landlord.
-Rarely did the tenants complain to the landlord. (or is it: The tenants rarely complained to the landlord.)

There is some food in the refrigerator.
-Scarcely does the refrigerator have some food. (Or is it: There is scarcely some food in the refrigerator.)

Marie studies with Ken.

-Seldom does Marie study with Ken. (or is it: Marie seldom studies with Ken.)
Both are correct.

The farmers were able to support their families.
-Just barely were the farmers able to support their families. (or is it: The farmers were barely able to support their families.)
The second one (in parentheses) is correct.

The patient could speak.
-Hardly could the patient speak. (or is it: The patient could hardly speak.)
The second one (in parentheses) is correct.

The tenants complained to the landlord.
-Rarely did the tenants complain to the landlord. (or is it: The tenants rarely complained to the landlord.)
Both are correct.

There is some food in the refrigerator.
What do you think for this one?

Actually for that one I put

Scarcely does the refrigerator have some food. or There is scarcely some food in the refrigerator.

I am confused because I read in my grammar book that if there is a helping verb in the sentence, you simply reverse the subject and the verb but if there is no helping verb you add a form of "do" taking all the information from the main verb and leaving the main verb in its base form.

In this sense isn't "Barely were the farmers able to support their families" "Hardly could the patient speak" correct?

They are correct grammatically, but very awkward. Those sentence structures are seldom used.

For the first statement, "Marie studies with Ken," the adverb "seldom" can be placed in front of the subject "Marie." Therefore, both options are correct:

1. Seldom does Marie study with Ken.
2. Marie seldom studies with Ken.

For the second statement, "The farmers were able to support their families," the adverb "just barely" can be placed in front of the subject "the farmers." Therefore, both options are correct:
1. Just barely were the farmers able to support their families.
2. The farmers were barely able to support their families.

For the third statement, "The patient could speak," the adverb "hardly" can be placed in front of the subject "the patient." Therefore, both options are correct:
1. Hardly could the patient speak.
2. The patient could hardly speak.

For the fourth statement, "The tenants complained to the landlord," the adverb "rarely" can be placed in front of the subject "the tenants." Therefore, both options are correct:
1. Rarely did the tenants complain to the landlord.
2. The tenants rarely complained to the landlord.

For the fifth statement, "There is some food in the refrigerator," the adverb "scarcely" cannot be placed in front of the subject "the refrigerator." Therefore, the correct option is:
- There is scarcely some food in the refrigerator.