Foreign female name that doesn't end in a normal Russian female name ending. If it were... Norma, then yeah, you'd decline it (У Нормы что-то). Foreign masculine names do decline as well, even if they don't have traditional Russian male name endings (for instance, У Обамы for Obama).
That's wrong, actually. There are often other indications, and this is one of those cases. The use of "есть" makes this a question about existence, rather than location - does butter exist with her, i.e. does she have (any) butter?
If this was "does Jenny have the butter?", that's a question about some specific butter, asking if Jenny has it, and would be translated as "масло у Дженни?"
Масло is the nominative singular of the word. It is a neuter gender word, as are most words ending in -o. Масла is the genitive singular declension of the word. You'd use it in instances where genitive is required ("a drop of oil" - капля масла / "I don't have oil" - у меня нет масла).
I'm sorry if I'm nitpicking, but just for clarity's sake:
- "есть" on its own cannot mean "have". It's the construction "у X есть" that is translated as "X has/have". In this sentence it literally means "there is", so the literal meaning of "У дженни есть масло" is "At Jenny there is butter".
- the infinitive form of the verb "eat" is "есть"; "ест" (without the soft sign) is the third person singular form: (he/she/it) is eating.
Да, в русском языке слово "масло" используется и для "butter", и для "oil". Однако часто вместе с уточнением: "сливочное масло" ("butter"), "растительное масло" (а можно назвать конкретный вид растительного масла: подсолнечное масло, оливковое, и т.д. - в значении "oil"). А можно просто "масло", и из контекста чаще всего понятно, о чём идёт речь.