More money supply is actually equivalent to saying "cheaper debt". Cheaper debt means, more loans in the economy. More loans in the economy stimulates demands here and there, be them related to stocks, to consumption goods or to productive goods (but let's maintain the latter constant). More demands (with a constant level of supply) means increases in prices: of stocks or of consumption goods; actually all this depends on where (stimulated) demands go.
Nominal rates are price-like objects and are subject as well to augmentations (inflation), depending on companies' strategy for dealing with increases in demands, their supply-capacity, their marketing considerations and the competition intensity in the sector. Be those as they are, inflation generates a downward pressure on real rates (of return). This downward pressure may be counterbalanced if companies chose to adapt their nominal rates (prices) as well, or not.
As increase in inflation would cause nominal interest rate to increase and also may cause firms' nominal profit and dividend to increase, [...]
This depends on whether companies want to keep their real rates of return constant. This is not "mechanic", but companies' strategy-based. If they chose to do so, i.e. to keep constant their real rates of return, this will be reflected in the nominal increase of their profits (real profits will thus remain constant).
[...] does this mean that the nominal stock price will not change due to inflation change.
The intellectual link you are doing here is nothing but obvious nor mechanic, and it appears to reflect your confusion regarding the subject. This is possible but not for unequivocal reasons: this ultimately depends on (i) where (stimulated) demands go or (ii) how the "market" perceives (within this context of exogenous/political-based increase in money supply) the strategy of the considered company. E.g. If the market "thinks" that the chosen strategy is the good one, they will probably wants more of company's stocks, which in turn will ceteris paribus increase their prices...