Can funeral services take place on a Saturday afternoon?

Sure, why not. The only objection would be if it was Good Friday, which has the churches tied- up with honoring the Death of Christ. as a general rule- any bans on funeral masses are more for traffic-control than any other reason. There are regularily scheduled masses on Sundays, and also on major religious holidays. There is not problem with Fridays unless it is a major religous holiday- such as Good Friday.