Yes, he is an ordained minister of the Assemblies of God. His book is used in many Bible Colleges of other denominations. They even use it at Dallas Theological University which is very much anti pentecostal/charismatic, but they know a good book on heremeneutics when they read one.
As to his views on Arminianism; I don't know what Arminius taught that Fee agrees with or disagrees with.
I suppose you would be correct in saying that the Assemblies of God position on the possibility of a saint backsliding to the point of apostacy is more similar to the Arminianism view than the Calvinist view but I don't think it would be correct to say that the AOG position is that of Arminiansim.
Attempting to put everyone in a two boxes theologically is not how things really are. That is a faulty sort of tunnel vision people fall into that is unnecessary and rude to their fellows Christians.
If you want to know what the AOG position is on any particular common doctrine you can find good explanations with scriptures and interpretations from their link on their Statement of Faith and their link to their Position Papers which are published whenever there is a need to address something controversial in the churches.
https://ag.org/beliefs/statement-of-fundamental-truths
https://ag.org/Beliefs/Position-Papers
Gordon Fee disagrees with the AOG on some of their statements. And I think I might agree with him. I think he could help the AOG rewrite their Statement of Fundamental Truths. They could use a more scholarly explanation.
From Wikipedia;
Fee is a Pentecostal; nevertheless, he has disagreed with some long held and deeply cherished Pentecostal beliefs. Specifically, he has questioned article 7 of the
Assemblies of God Statement of Fundamental Truths, which articulates a classical Pentecostal understanding of
baptism in the Holy Spirit as subsequent to and separate from
Christian conversion. In "Baptism in the Holy Spirit: The Issue of Separability and Subsequence", Fee writes that there is little biblical evidence to prove the traditional Pentecostal doctrinal position.
[9]
On the other hand, he maintains that "the Pentecostal experience itself can be defended on exegetical grounds as a thoroughly biblical phenomenon".
[10] Fee believes that in the early church, the Pentecostal experience was an expected part of conversion:
The crucial item in all this for the early church was the work of the Spirit; and [the empowerment for life], the dynamic empowering dimension with gifts, miracles, and evangelism (along with fruit and growth), was a normal part of their expectation and experience.
[11]
Fee believes the Spirit's empowerment is a necessary element in the life of the Church that has too often been neglected.
[12] It is this neglect, Fee argues, that led early Pentecostals to seek the presence and power of the Spirit in experiences which they identified as baptism in the Holy Spirit.
[13]