Hola Sound

When we use "lo mismo" in this context (the one Steven was presenting in his question) that is an idiomatic phrase meaning "maybe" - it doesn't have that meaning of "igual/iguales". 

For your meaning of "mismo", meaning "the same", we use it like this:

Mi coche es igual / Mi coche es el mismo = My car is the same

Las maletas son iguales / Las maletas son las mismas = The suitcases are the same

etc, i.e. with agreement, using el mismo, la misma, los mismos, las mismas, or, igual and iguales, depending on the gender and number (sing.or plural) of the noun they are modifying.

I hope this clarified it.

Saludos

Hola Steven

Yes, you can. Quizás and Lo mismo are synonyms, with lo mismo being more colloquial. 

Saludos