1. Sorry for keep you waiting or sorry for keeping you waiting. 'Sorry for KEEPING you waiting' 'For' is a preposition, and it is always followed by a noun or a gerund (..ing) form. 2. When we use "best" and "the best" 'Best' a superlative form (like 'biggest' or 'most expensive'), so it is usually preceded by 'the'. There are a few exceptions - such as expressions like 'It would be best if you went home' - but in most all other cases, you should use 'the'. We use 'the' when referring to something specific rather than general, and 'the best restaurant' or 'the best student' are specific. You can also replace 'the' with other determiners, such as possessives e.g. 'This is my best dress', but you rarely have 'best' without some kind of determiner before it. 3." The use of" or "the usage of" Don't worry about it. Most native speakers aren't sure, either. Some people just say 'usage' to sound more academic. If in doubt, just say 'use'.

1. sorry for keeping you waiting 2. "the best" serves as a noun. It implies "the best person/employee/etc" 3. the usage of

1. Always use the -ing form, never the base form or infinitive, after any preposition.