Are the introns present in a nascent rna molecule removed simultaneously or are they removed in some sort of sequential fashion or is removal completely random?
There are two different ways to interpret this question:
Does the spliceosome splice all introns of an mRNA simultaneously or sequentially?
Can a spliced mRNA be re-spliced?
How does a spliceosome proceed along the mRNA?
According to this review:
splicing generally proceeds in a 5′ to 3′ direction, although neighboring introns are not always excised in this order, nor are all introns completely removed during synthesis (36).
Splicing tends to happen immediately following transcription of introns, so it is to some extent necessarily sequential (same review):
Time course measurements by RT-PCR of multiple pre-RNA species synthesized after reversing 3 hours of DRB inhibition have shown that intron excision occurs within 5 – 10 minutes of synthesis of the downstream neighboring exon, irrespective of the length of the intron, the length of the gene or whether the intron is excised by the major or minor spliceosome (42).
Thus, it is not physically possible in many cases to splice all the introns of a RNA simultaneously, because splicing begins before pre-mRNA synthesis is even complete.
Re-splicing mature/spliced mRNA
There are a few different mechanisms by which RNA can be spliced at more than one point. For example, ribozyme splicing occurs in a spliceosome-independent fashion, so an mRNA with a ribozyme in it and also non-ribozyme introns will necessarily have multiple rounds of splicing.
There is additionally so-called recursive splicing of very long genes/introns. This is when a spliced intron must be handled in multiple rounds due to its length/complexity; it's a bit involved so I won't go into it here.