Your two questions are ones that any foreigner who is considering getting married in Thailand should know the answers to.
1) What claim on my property would she have if we were married in Thailand?
The law in Thailand states that all property in any form which belongs to you prior to the marriage still belongs to you should you later divorce. Let's say you have 2mm baht in the bank before you get married. If you spend that 2mm baht to purchase a house and land after you are married, that property under Thai law belongs to you. There is also wording in the law which states that property which is acquired during the marriage which replaces property which you owned prior to the marriage is also considered your property.
However, the law also states that all income, including interest income, which either party earns during the marriage is equally owned by both the husband and the wife. This would technically include income generated from rental property, bank accounts, businesses, lottery winnings, etc. back home. Finally, the law states that in the event that evidence cannot be produced that the property which was acquired during the marriage was purchased with individual money, then the law presumes that the property is marital property. So you need to keep good records.
There is an enormous amount of misinformation floating around the internet on this subject and many Thai lawyers misinterpret the law as well. The root of this confusion stems from the wording of the thai law which reads everything which the couple "ได้" is marital property. "ได้" can be translated as "gets" or "obtains" and many casual readers of the law misinterpret this to mean that anything which the marital couple purchases during the marriage is thus automatically marital property, which must be divided equally if the couple divorces. This is totally incorrect.
2) How would a divorce affect my marriage visa would I then only be able to stay on a tourist visa for 3 months + 3 months extension?
If you are over 50 years old, you could easily convert your marriage visa to a retirement visa. The only change would be that the financial requirement for a bank deposit would be increased from 400,000 to 800,000 baht. Some people have questioned why Thailand requires more money for someone to retire than they require for someone to care for a family. I don't know this for sure, but I suspect that the reason is because an older retiree is more likely to have health problems and the Thai government doesn't want to be stuck with the bill if medical care is required. It's not because the Thai government is trying to discourage retirees from moving to Thailand.
If you are not over 50, and you cannot get a work visa, I think your only options are 90 day visa runs, but I am not 100% certain about this.
Regarding purchasing property (land) this is rife with moral hazard, as except for very few exceptions you cannot legally buy land in Thailand, and if you try to get around this law, you are going to have to register the land in someone else's name. If you decide to do this, my stern advice would be to keep the amount and cost of the land and any house to an amount you could walk away from if your marriage goes south. Trying to recover your investment is going to be next to impossible. For this reason, you would be far better off buying a condo in your name. I know this does not appeal to many people, including me, but at least that way the property would be registered in your name, and there wouldn't be any dispute about ownership in the event of divorce. If your situation is financially complicated or you have considerable income overseas which will continue during your marriage, I would recommend consulting with an attorney and making a pre-nuptual agreement.
I didn't pull out my file on Thai marital property law, but if anyone wants more specific legal reference information, I would be willing to provide it. Hope this helps.