papering over lining paper

If all the previous work has been done to a good standard then i cant forsee any problems. I would use a good quality ready mixed wallpaper adhesive that has less water content than the shaky sachets

It is more efficient + will produce a better finish to strip. It is possible, but I would not paper over any other previously hung paper, with a finish paper, unless I was 100% sure it was hung + stuck properly. There is a wet test you can do, by spraying the paper all over with water, if any areas bubble then it needs stripping. Also the painted surface would need keying. The problem would be if you paper over old paper, the paste under the old paper can be deactivated by fresh wet paste + would therefore bubble.

applying wallpaper over the painted lining paper is not a problem if your walls are cross lined (from side to side) if the lining paper has been hung like you would hang any finish paper this is fine too as long as your joints are not on the same joint as the lining paper

It is possible to paper over vinyl silk paint. But it must be sanded first to degloss. Otherwise your paper will not adhere properly. Personally i would preffer to strip and reline the walls. As i personally think this is best practice. But it is possible to paint over after deglossing.

Strip linei gpaper off . You have a chance it will bubble ans it makes it hard to rectify

best course of action here would be to remove the silk emulsioned lining paper. However, you could bond the entire area with diluted pva (polybond) the day before you intend to hang the paper allowing 24 hours for the bond and the lining paper to dry out. this will allow any bubbling of the lining paper to dry back and will avoid the neseccity of "keying" the silk emulsion.