It's going to be hard for me to post here on this week because I'm busy with college, but I'll try anyway.
Yes... as Cuc mentioned, the Paradise from Neo-Traditionalism of Japan is really Sukhavati, aka: Gokuraku (極楽, "Ultimate Bliss"), because I can find the two kanjis on the japanese text.
The celestial world Tenkai (天界) is written in different Kanji than Sukhavati (極楽) so, the two places are most likely not the same. Seems like Tenkai is just a name for the celestial world/heaven in general, it's even used for it's western counterpart, as TheNewGuy mentioned. Sukhavati on other hand, seems to be a realm even higher than Tenkai, only achieved by the purest among pure beings. Hence why it's called "Ultimate Bliss". From what I can see, it's out of reach even for most of the Celestials themselves.
And no, Bhava-agra and Sukhavati are not the same. The kanji is even different. (有頂天 x 極楽) The former is just a place inside of Tenkai. To explain it better, I'll try a simple analogy. Think about Tenkai as the "country" while Bhava-agra is a "state" inside said country. As it was aforementioned, Tenkai is a collection of many realms above earth. Bhava-agra is just one among them.
Now, I can't guarantee if Tenkai is one of the realms of Samsara, but it might be. Even though according to Buddhism, the "heaven" of the six worlds is written as Tendō (天道) which shares a different kanji than Tenkai. Those two are even sepparate articles on japanese wikipedia, as it can be seen below:
Tendō 天道 Tenkai 天界More info about the six worlds of Samsara:
1) Beings in Hell. Naraka-gati in Sanskrit. Jigokudō 地獄道 in Japanese. The lowest and worst realm, wracked by torture and characterized by aggression.
2) Hungry Ghosts. Preta-gati in Sanskrit. Gakidō 餓鬼道 in Japanese. The realm of hungry spirits; characterized by great craving and eternal starvation.
3) Animals. Tiryagyoni-gati in Sanskrit. Chikushōdō 畜生道 in Japanese. The realm of animals and livestock, characterized by stupidity and servitude.
4) Asura. Asura-gati in Sanskrit. Ashuradō 阿修羅道 in Japanese. The realm of anger, jealousy, and constant war; the Asura (Ashura) are demigods, semi-blessed beings; they are powerful, fierce and quarrelsome; like humans, they are partly good and partly evil.
5) Humans. Manusya-gati in Sanskrit. Nindō 人道 in Japanese. The human realm; beings who are both good and evil; enlightenment is within their grasp, yet most are blinded and consumed by their desires.
6) Deva. Deva-gati in Sanskrit. Tendō 天道 in Japanese. The realm of heavenly beings filled with pleasure; the deva hold godlike powers; some reign over celestial kingdoms; most live in delightful happiness and splendor; they live for countless ages, but even the Deva belong to the world of suffering (samsara) -- for their powers blind them to the world of suffering and fill them with pride -- and thus even the Deva grow old and die; some say that because their pleasure is greatest, so too is their misery.
Also, while it's only mentioned through one of Keine's spell cards, I still assume Takamagahara exists in Touhou. We can't guarantee anything, but considering Amaterasu herself actually exists in Touhou (it was proven through Silent Sinner in Blue's chapter 16), then I can't think of any place for her to reside other than Takamagahara, so, I suppose keine's spell left implicit the existence of said place.
Probably it turned out a bit confusing, but I tried my best.