Hi @mjz5448,
For your first question, the response from @MathStatChem will help you analyze your experiments with covariates added a-posteriori. You can check the Evaluate Designs and Multivariate platforms to evaluate the correlations between your original factors and the added covariate, to check any blind spot that this addition may create (complete aliases between specific model term and main effect of the covariate factor for example). Specific analysis and models able to handle multicollinearity may be required : Partial Least Squares, Generalized Regression with penalization through Ridge/Elastic Net methods, use of robust Machine Learning algorithm like Bootstrap Forest/Predictor Screening, etc...
For your second question, I would recommend reading these topics with similar issue :
Covariates in defined order in custom design
Incorporate Time lag in DoE
The first topic describes how to create a time-robust DoE by taking into account time as a covariate directly in the DoE creation.
I hope this answer will complement the other and help you,
Victor GUILLER
Scientific Expertise Engineer
L'Oréal - Data & Analytics