No, friendship will not be affected.
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No Pokémon are not capable of evolving while the Daycare Couple are taking care of your Pokémon you will need to take them out of the Daycare in order to evolve your Pokémon.
There is a Celadon Mansion its next to the Pokemon center on the first floor you will find an old lady near some Pokemon talk to her to receive some tea give this to the security guard blocking saffron city he will let you pass after taking the tea.
Taking "WHITE APRICORNS" to Kurt.
The following Pokemon evolve solely through friendship, and are unable to evolve through any other means:Buneary, into LopunnyChansey, into BlisseyCleffa, into ClefairyGolbat, into CrobatIgglybuff, into JigglypuffMunchlax, into SnorlaxPichu, into PikachuTogepi, into TogeticRiolu, into Lucario (during the day time 4am - 8pm)Elekid, into ElectabuzzMagby, into MagmarEevee, into Umbreon or Espeon, either during the night or dayBudew, into Roselia (during the day time 4am - 8pm)Chingling, into Chimecho (during the night time 8pm - 4am)You can help it like you by walking around with it in your party, taking it to Amity square, giving it masages, taking it to the spa, avoid letting it faint, giving it a special hold item and feeding it berries.
If your are taking the elevator up to go see Jasmine(?) and the Amphraos, then yo can't get in, you have to climb the stairs and they will lead you to the center of the room that the girl is in. That is if I remember correctly, not sure if that is what you mean't or not. Hope I helped.