If Jesus is "a god" would not Jehovah’s Witnesses be polytheists?

No, of course Jehovah's Witnesses do not consider themselves to be polytheists. That is because they make sure they do not give any worship to Jesus Christ. It is strictly 'taboo' for any JW to pray to Jesus (as prayer is an act of worship), or to bow down on one's knees or to prostrate themselves in the name of Jesus (which is an act of worship). They speak of metaphoric 'bowing down' in Jesus' name, but it must never be literal. They speak of an attitude of respect to Jesus but ensure that that never becomes a worshipful attitude. They speak of obedience to Jesus' commands as a sign of their respect for him but at every point, their respect for, and honour of Jehovah God must always be greater than that which they have for Jesus Christ, because they maintain that Jehovah created Jesus as a separate being, distinct from himself. They know the Bible condemns polytheism, or even worship of more than one God, so they are at pains to stress that they never worship Jesus either as God, or as 'a god'.

To demonstrate their stance on refusing to pray to Jesus, consider their treatment of Acts 7 verse 59 which says, "While they were stoning him, Stephen prayed, 'Lord Jesus, receive my spirit'." But JWs have been told that no, Stephen was NOT praying to Jesus. That is why their NWT renders this verse as, "And they went on casting stones at Stephen as he made appeal and said: 'Lord Jesus, receive my spirit'."

Notice how the word 'prayer' is avoided? The Greek word for "calling upon" is in the text used by the JWs. However, all JWs know that Jesus was not physically present when Stephen called upon him after having had a vision of both God and Jesus. They know the resurrected Christ was in heaven. They also know that the only way you can call upon God or Christ, who are not physically present, is to pray to them. Here is what their Insight on the Scriptures says, Vol. II p 667:

"The entire Scriptural record testifies that Jehovah is the One to whom prayer should be directed... Though some claim that prayer may properly be addressed to others, such as to God's Son, the evidence is emphatically to the contrary. True, there are rare instances in which words are addressed to Jesus Christ in heaven. Stephen, when about to die, appealed to Jesus, saying, "Lord Jesus, receive my spirit." (Ac 7:59) However, the context reveals a circumstance giving basis for this exceptional expression. Stephen at that very time had a vision of 'Jesus standing at God's right hand,' and evidently reacting as if he were in Jesus' presence, he felt free to speak this plea to the one whom he recognized as the head of the Christian congregation."

So although the JWs admit Stephen was calling out to Jesus in heaven, they refuse to say it was a prayer to Jesus.

I will not give further quotes on the other points, for I am quietly confident that JWs will be eager to provide ample quotes from their official web-site that will conclusively show that they are confident their refusal to worship Christ to any degree whatsoever does not contradict them giving him a merely titular ascription of being "a god". Although it is worship that differentiates deity from creatures, JWs believe that simply giving Jesus a title of "a god", while ensuring their respect for him always stops short of worship, overcomes this theological problem of the Bible calling Christ "the Mighty God" (Isaiah 9:6) and (in their NWT) "a god" in John 1:1, despite verse 3 stating that he "made everything that was made".

As for the specific question you ask: "is Jesus Christ a true god, or a false god?" - JWs would never say Jesus must therefore be a false god (given your points). They think Jesus is 'a mighty one' and would argue that 'god' in lower case refers to that, without that 'mighty one' requiring any worship. It might be worth asking a further question on why, then, Jehovah God is ALSO called "the Mighty God" in Isaiah 10:21, a few verses on from the Son being given that same accolade.

Do Jehovah’s Witnesses consider themselves to be polytheists? No, because they do not worship Jesus. They worship only Jehovah God. Jesus is not the Almighty God, but is merely “a god” who was created by Jehovah as a mighty spirit creature. He is divine but he is inferior to Jehovah God. Here is the official Jehovah’s Witness view from the February 2006 Awake article, The Bible’s Viewpoint: Is There Only One True God?

Jesus, the Angels, and the Devil: The Scriptures do at times refer to actual persons as gods. However, a careful examination clearly reveals that the term “god” in these instances is not intended to designate these individuals as deities. Rather, in the original languages in which the Bible was written, the term “god” was also used to describe a mighty person or an individual who is divine or closely associated with the Almighty God. For example, some Bible verses allude to Jesus Christ as a god. (Isaiah 9:6, 7; John 1:1, 18) Does this mean that Jesus is to be worshipped? Jesus himself said: “It is Jehovah your God you must worship, and it is to him alone you must render sacred service.” (Luke 4:8) Clearly, although Jesus is mighty in power and divine in nature, the Bible does not portray him as an object of worship. Source: https://wol.jw.org/en/wol/d/r1/lp-e/102006049

Is Jesus a true god or a false god? Here is their explanation as given in Questions From Readers 1986: ▪ How could Jesus be “a god” who was created by Jehovah when in Isaiah 43:10 Jehovah says: “Before me there was no God formed, and after me there continued to be none”?

The Lord Jesus Christ is no false god, no demon god, no mere idol. He ‘is the reflection of Jehovah God’s glory.’ (Hebrews 1:3) Thus it is fitting for John 1:1 to acknowledge Jesus as “a god,” or “godlike” (Johannes Schneider). Source: https://wol.jw.org/en/wol/d/r1/lp-e/1986491

Is this first spirit creature created by God and described as "a god" at John 1:1 a true god or a false god, and what is his nature? Now we come to the real issue – the Jehovah’s Witness belief that Jehovah created Jesus as a mighty spirit creature. If they are right, then the nature of Jesus must be that of a created angel (who they say is known in heaven as Michael the Archangel). And the Bible says we must not worship any created angel (Revelation 19:10). Therefore, if Jesus is a created spirit creature then the Witnesses do right not to worship him.

But the Bible also says that God has never called any created angel his Son, or claimed to be his Father (Hebrews 1:5).

Yet all God’s angels are told to worship his Son (Hebrews 1:6).

Was Jesus created before coming to earth? That is the only question that demands our attention when establishing who Jesus REALLY is. But you have not asked that question in such a way that Trinitarian Christians can answer from the Bible.