Spellings

Feign is the correct spelling meaning to pretend or simulate. The 'ei' combination makes the 'ay' sound. It's a concise word often used in phrases like "feign ignorance" or "feign illness."

Freer means able to act at will.

 Grammar is the correct spelling.

Gardener is the correct spelling for someone who tends a garden. The word uses 'er' suffix (person who does) attached to 'garden'. Note the 'e' after 'gard' before 'n' - it's garden-er, not gard-n-er.

Gymnasium is the correct spelling for a large room used for physical exercise and sports. The other options are misspelled versions.

Hypocrite is the correct spelling for a person who pretends to have virtues they don't possess. The other options are misspelled.

Hideous is the correct spelling meaning extremely ugly or repulsive. The other options are misspelled.

Immanent is the correct spelling (philosophical term meaning 'existing within' or 'inherent'). Imminent means 'about to happen'.

Immovable is the correct spelling (unable to be moved). It has double 'm' like the root word 'move'.

Fibre is the correct British spelling (fiber in American English). The other options are misspelled.

Excellence is the correct spelling meaning superior quality. The other options are misspelled.

Apparently 

The correct spelling is 'Embarrassment' with two r's and two s's. The root word is 'embarrass' (with double r and double s), and the suffix '-ment' is added directly without changing the spelling. Common misspellings include 'Embaresment' (wrong vowel), 'Embaressment' (missing one r), and 'Emmbarresment' (extra m, wrong vowel). The double consonants are preserved when adding the suffix.

Successor is the correct spelling for someone who follows another in an office or position. The other options contain phonetic errors: saccessor drops the 'c', succeser replaces 'c' with 's', and suksessor misplaces the 'k' sound.

The correct spelling is 'preservation' with 'e' after 'v' and 'ation' at the end. The word comes from 'preserve' + the suffix '-ation'. Options B, C, and D all contain spelling errors in the middle or end of the word.