All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ʻalayhi wa sallam, is His slave and Messenger.
As for your first question, there is no harm in performing the funeral prayer after the ʻAsr; the scholars did not differ in opinion in this regard. Rather, they differed regarding performing the funeral prayer at the three specified times when it is deemed prohibited to pray the funeral prayer, namely, sunrise, sunset, and when the sun is at its meridian (middle of the sky).
Ibn Qudaamah wrote:
“Issue no. 1020: Offering the funeral prayer. With regard to offering the funeral prayer after the Fajr prayer until the sun rises and after the ʻAsr until the sun draws near to setting, there is no difference of opinion among the scholars concerning it. Ibn Al-Munthir said, ‘The consensus of the Muslims is that the funeral prayer may be offered after the ʻAsr and the Fajr. With regard to offering the funeral prayer at the three times mentioned in the hadeeth of ʻUqbah ibn ʻAamir (There were three times at which Allah's Messenger forbade us to pray, or bury our dead: When the sun begins to rise till it is fully up, when the sun is at its height at midday till it passes over the meridian, and when the sun draws near to setting till it sets.), it is not permissible.’ This was mentioned by Al-Qaadhi and others. Al-Athram said, ‘I asked Abu ʻAbdullah about offering the funeral prayer when the sun has just risen. He said, 'As for (doing so) when the sun has just risen, I do not like that.' Then he quoted the hadeeth of ʻUqbah ibn ʻAamir.’ A similar opinion was narrated on the authority of Jaabir and Ibn ʻUmar. This was quoted by Maalik in Al-Muwatta' on the authority of Ibn ʻUmar. Al-Khattaabi said, ‘This is the view of the majority of the scholars.’ Abu Al-Khattaab said, narrating a different report from Ahmad, that offering the funeral prayer is permissible at all times when prayer is not allowed. This is the view of Ash-Shaafiʻi because it is a prayer that is permitted after the Fajr and the ʻAsr, so it is permitted at all other times, like the obligatory prayers.” [Al-Mughni]
Allah knows best.