Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Do the Jinn have anything to do with the disappearance of objects?
Jinn are one of Allah creatures, and whosoever lost anything should look for it and never accuse niether the Jinn nor humans of stealing it. And Allah Knows Best.
Is it permissible to offer the Eid sacrifice in a non-Muslim country?
Eid sacrifice is permissible anywhere, and Islamic Sharia hasn`t determined that it should be in an Islamic country, but poor Muslims should be given a share in order for it to be valid since it is an act of worship. A portion of that Eid sacrifice should be given at least to one poor Muslim, and if that wasn`t possible then the one offering it should consume it along with his family.
Is there a solution to put an end to thinking of worries during prayer?
Firstly, make ablution after the time for prayer begins and busy yourself with remembering Allah, The Exalted, before the iqaamah (start of prayer).In order to become humbly submissive during prayer, you must perform prayer in congregation. After the prayer ends, stay in your place and read the post-prayer remembrances (Adhkaar) and make supplication to Allah, The Exalted.