Cell penetrating peptides disrupt the cell membrane and enter inside the cells. It does not recognize the overexpression of protein on the cell surface. For further details you can see the article in the attachment
It is unlikely but I believe no one can say for sure. Disruption of the membrane can change cellular physiology and can effect ion channels. There are long term studies on expression of cargo that I know of. My work with penetratin has shown massive effects on Ca-activated chloride channels (see below).
Yes indeed, In my study on TAT peptide, this peptide could change (decrease) the expression level of cargo in comparison with the expression of cargo alone (as control).
Also, the high positive charge of CPPs can affect the expression of cargo, too. For example in my study the protein cargo had high positive charge and when it fused to a CPP, resulted recombinant protein expressed as insoluble protein and I had to purify that by use of urea. While, the protein cargo was expressed as a soluble protein when it was alone (native protein).
This so important specially when your protein cargo is enzyme and you want it to remain functional.
That is very interesting. I did not see any obvious effect of TAT peptide in oocytes, as in my report above. I think many biochemical studies have just used TAT or penetration peptides without or avoided reporting any/potential side effects.