As someone who primarily plays the game as solo hotseat, my first advice would be to start small. Even on a standard size map, you're essentially playing eight games at once. This matters both in terms of time to complete a game and in terms of having to reacquaint yourself each turn with the strategy each civ is pursuing. Also, if you can get through games faster, you can better adapt your house rules to situations that you see causing problems rather than having to speculate about which ones might.
Regarding your specific house rules:
1.) I de-facto avoid surprise wars as well. This mostly only matters for preventing early captures of civilian units, though. Keeping a denunciation active on each civ you want the option of declaring war on isn't difficult.
2.) I don't ban this absolutely, but my civs are much stingier about trading away strategics than the AI.
3.) This sounds like a reasonable restriction, though I haven't tried it myself. I might consider an active trade route instead of a trading post.
4.) I'm not sure of the reasoning behind this restriction. I think allowing each civ to pursue the city states best fitting its strategy of one of the strengths of solo hotseat. A neighboring city state allied to a rival is an inviting opportunity for conquest, though, so targeting distant CS is risk, even without specific limitations.
5.) As with city states, I think allowing civs to focus on the wonders that best suit their strategy is one of the best features of solo hotseat. This also creates something of a self balancing mechanic, where pursuing the strongest most generally useful wonders is a bigger risk.
6.) With heroes, I think there's an interesting trade off between waiting for a strong/synergistic hero vs. grabbing heroes as fast as you can in the hopes of getting more of them. Guaranteeing every civ exactly one removes this trade-off, while still leaving significant imbalance between civs with stronger vs. weaker heroes. I mostly play with 8 or 9 civs, though, so there's less risk of a civ missing out completely.
7.) I think restricting GP purchases closes off a lot of interesting and valid strategies. The idea of "announcing" purchases makes sense if you feel this needs more explicit structure, though.
In general, it seems like a lot of your rules are designed around preventing you from biasing yourself towards a particular civ or outcome. I don't think this is really possible through any set of formal rules, there are just too many small decisions adding up. You just need to do your best while recognizing that human brains being what they are, some level of bias is inevitable.
A couple more points to consider:
-Religious combat is almost always a mistake for one player, since fighting and losing is so much worse than sitting back and letting opposing units do their thing. I generally just accept that religious combat won't happen, but if you want it to play an important role, you'll need house rules to support it.
-Similarly, you should consider whether you want to have any restrictions on declaring war to kill religious units.
-Civs late in the turn order can gain a strategic advantage in the world congress if you're too good at remembering your previous votes. I often take a break midway through the vote to mitigate this at least somewhat. You could also consider the discussions that leaders could have about coordinating votes. The whole world congress system is a mess regardless of game-mode, though, so I don't have a great solution regarding how to handle it.
