Does it reflect poorly on a plaintiff if they have filed a few claims in different situations in the past?

Based upon facts, one has nothing to do with the other and should have no bearing on the latter action. Depending on the Court and dates involved, it my be possible to search online by names of parties. There are several private services that offer this service as well. One may also do it the old fashioned way and go to Court and check the index. The other way is to simply ask the party in discovery if they have been involved in any lawsuits.

If the person only filed two lawsuits then that really doesn't mean much, especially if there is a gap of a few years between the suits. If a person has filed a dozen lawsuits, then that might certainly lead to questions intended to convince a jury that the person essentially is just constantly rolling the dice and hoping to win the legal lottery. Whether prior lawsuits can be searched online depends on how modern your local jurisdiction is and how long ago the prior suits happened.

Filing legitimate lawsuits should not have a negative impact on a plaintiff. However, a jury could consider that to be a negative if the information was ever submitted as evidence at trial - a good attorney could probably keep it out as irrelevant. But, filing multiple lawsuits that lack merit can have a negative impact as you could be branded a vexatious litigant - which would prevent you from filing further lawsuits unless you posted a bond or got permission from a court.