for guidance it is good and no problem and even needed. all prophets came for this.
but for asking forgiveness non-Muslims are two group:
some are believers (for example Christians) who do not have envy and enemty with Islam and for any reason could not know true Islam and if knew Islam without propaganda accepted it. for them there is no problem.
but for those who have envy and enmity with Islam it is prohibited.
مَا كَانَ لِلنَّبِيِّ وَالَّذِينَ آمَنُوا أَن يَسْتَغْفِرُوا لِلْمُشْرِكِينَ وَلَوْ كَانُوا أُولِي قُرْبَىٰ مِن بَعْدِ مَا تَبَيَّنَ لَهُمْ أَنَّهُمْ أَصْحَابُ الْجَحِيمِ
[9:113] Sahih International
It is not for the Prophet and those who have believed to ask forgiveness for the polytheists, even if they were relatives, after it has become clear to them that they are companions of Hellfire.
لَّا يَنْهَاكُمُ اللَّـهُ عَنِ الَّذِينَ لَمْ يُقَاتِلُوكُمْ فِي الدِّينِ وَلَمْ يُخْرِجُوكُم مِّن دِيَارِكُمْ أَن تَبَرُّوهُمْ وَتُقْسِطُوا إِلَيْهِمْ ۚ إِنَّ اللَّـهَ يُحِبُّ الْمُقْسِطِينَ
[60:8] Sahih International
Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly.
also we do not know how to pray God correct.
best prayers are passed to us from prophet and Ahl Bayt and it is better we use them and do not use prayers made by ourselves because prayers have many spiritual secrets and effects that we do not know.
best prayers ever: