Keeping this in consideration, does increasing sample size affect type 1 error?
Increasing sample size will reduce type II error and increase power but will not affect type I error which is fixed apriori in frequentist statistics.
Beside above, how do you minimize Type 1 and Type 2 error? There is a way, however, to minimize both type I and type II errors. All that is needed is simply to abandon significance testing. If one does not impose an artificial and potentially misleading dichotomous interpretation upon the data, one can reduce all type I and type II errors to zero.
Consequently, can you reduce the risk of a type 1 error by using a larger sample?
not large enough to reject the null hypothesis. You can reduce the risk of a Type I error by using a larger sample. There is always a possibility that the decision reached in a hypothesis test is incorrect. If other factors are held constant, as the sample size increases, the estimated standard error decreases.
How can the risk of type 1 error be reduced?
A p-value of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis. You can reduce your risk of committing a type I error by using a lower value for p. For example, a p-value of 0.01 would mean there is a 1% chance of committing a Type I error.