Are Indonesian 2018 earthquakes related?
I'll try to answer your second question using the earthquake catalog of the USGS. I encourage you to run your own queries, it's pretty fun and easy to use!



Here is a result of a query for 6+ magnitude earthquakes, starting from 2000, centered around the indonesian archipelago. There is a total of 435 events in the region during this period of time. Now you can download the list as a csv file and have a look at it to get some statistics.



If you sort the events by year, you'll see that there are between 11 (in 2017) and 35 (in 2007) events per year, with a mean of 21.75 events per year. It's hard to get a clear tendency from this graph, although it seems that there was a decrease in activity in the 2011-2018 period.



It gets clearer if you look only at 7+ earthquakes. In this period there are 54 events in the region, but you can see that the vast majority happened in the 2000's, culminating in 2010 with 8 events. Then there is the only year without a 7+ event (2011), and five years in a row with only one event per year. From this graph it also seems that there is an increase in the last two years, with already 3 events in 2019, but I would be careful interpreting this: we lack perspective, and 54 is quite a low number to do a statistically robust analysis.

So from this I'd say there might be an increased seismic activity in the region, although it's too soon to tell for sure. Only time will tell, unfortunately.

Edit: The first question is beyond my competence. It is known that earthquakes redistribute the stress in the lithosphere (see the review by Hardebeck &amp; Okada, 2018). But the tectonic setting is really complicated in Indonesia, with lots of small plates and some unique features, like the divergent double subduction in the Molucca sea (Zhang et al., 2017)... So it's hard to tell if an earthquake here could trigger an earthquake there by modifying the regional stress field.