Greetings, dear ROP, and peace to you!
Demons do exist; they are merely spirit beings and can be both good or bad (the term comes from the word "daemon" which simply means "spirit"). There is nothing to fear from either, though, good spirits OR "demons"... as spirit beings only have the power you give them. If you are not a person of spirit/heart/mind that would, then there's nothing they can do TO you - they are impotent as to man in and of themselves and must have power to overtake/possess conferred upon them. Either by God or by the person themselves.
Also, you cannot "contract" a demon simply by inviting one. Although your mouth may say "come," your heart/mind/spirit may not be (as) open as you think. It works that way with both good and bad spirits (hence, those who call upon JAH/Christ... and yet, do not receive an indwelling - their hearts/minds/spirit don't permit it - such are not "prepared"... meaning, clean enough... for such to occur. One must first cleanse the INSIDE of the cup - of hatred, hypocrisies, jealousies, envies, murders, adulteries... what have you).
I cannot share with you exactly HOW one can contract a demon - that would be absolutely unloving, given the risk for such to occur should one follow the information. I would be like me showing a 3-three-year-old how to load and shoot a gun, and then leave him/her alone with the loaded gun. But please don't fool yourself into thinking it CAN'T be done - it absolutely can. Which might be why some here are lovingly cautioning you.
As for those situations where healings and other "miracles" are performed, ones should keep a couple/few things in mind:
1. Unless those performing the events actually knew you were coming prior to, it makes no sense that EVERYONE else experienced some kind of phenomenon, except you. That would suggest that EVERYONE was faking, except you. Why would EVERYONE do that... unless they knew ahead of time that YOU were coming? Meaning, you were the only one(s) who weren't "in on it." Not logical or rational.
2. Not all who profess to obtain the gift of holy spirit that allows such miracles do. Certainly, if a healing took place it is from God (because it is a granting of a modicum of LIFE that causes the healing)... and so rather than be poo-poo'd one should consider REJOICING that someone who once was ill has been healed. Whether you believe HOW that occurred or not - should not the point be that they WERE healed, such that rejoicing... and not lamenting and fault-finding... should take place?
3. There are those who claim various spiritual "gifts"; however, such are NOT from God... but are actually powers received from another (spirit) "source"... and so "stolen." The thing with the thief/thieves who grant these gifts though, is that they always, ALWAYS exact a price, and almost always one too great to pay. Usually, it is one's eternal life... by means of exacting one's spirit (energy/life force).
I hope this helps and, again, peace to you!
A doulos of Christ,