@rms: If the options reset when changing from Theme Options, then it looks like it is your server issue. Some server block saving HTML data. I am afraid this is the case. Customizer handles options differently(by encoding and decoding), so this will not be a problem there. You can use Customizer as it has all the features of Theme Options and further, live preview. We will depreciate/remove theme options in the future.
@venus: You can reset your settings to default by going to Appearance=> Customize=> Reset All Settings =>Check to reset all settings to default
Please bear in mind that all your settings will be lost
I cannot understand your second question. If you switched theme, then switch back to previous theme, your settings/options will be there. Save it somewhere in notepad or other text editors and then reuse it.
Regards,
Pratik