Is the suicide of a moribund individual to be considered group selection?

Yes, group selection could have been selecting for suicidal behaviour.

[D]oes group selection require an intentional formation of a group?

There is clearly no need for intention or consciousness for group selection to occurs (e.g. Aviles 1986).

The majority of people working in social evolution agree that kin selection and group selection are the same thing (Lehmann et al. 2007; Abbot et al. 2013). However, people's intuition often fail when talking about group selection while it is not too bad when talking about kin selection (H. Kokko during a speech and L. Lehmann personal communication).

It depends on what form of group selection you are talking about.

Group selection carries a lot of baggage and can refer to two very distinct concepts. Concepts of group selection comes in two forms type 1, selection occurring on the group level, and type 2 selection on the group level that produces adaptations in said group or organism. The latter is the traditional usage of "group selection" the first(type 1) is now commonly (and confusingly) referred to as multi-level selection. (type 1 and type 2 are my terms I am using them to keep the two concepts identifiable)

Type 2 aka multi-level selection

Group selection (type 2) is simply selective pressures that occur above the individual level, kin selection could be seen as a form of this or it could not. It is still producing advantages and disadvantages to the genes and genes are still acting as the basic unit of evolution. Selection is occurring between groups with the differences between the groups being a product of the genes of the individuals within those groups. The genes are still favored or unfavored there is just many levels on which that the genes products can manifest. This models of group selection are basically just another form of gene based selection and adaptation it just adds another layer in which selection can occur.

Now few argue this form of group selection could not occur just that it would be swamped by normal gene based selection in most instances. There are genes known that are horribly detrimental to the individual and population in return for greatly favoring their own spread, the famous R2D2 gene in mice is an example.

Bacteria can be problematic in this as relatedness may not be a good measure of whether they share the same genes, and kin selection only requires shared genes. Could the behavior in bacteria be group selection in this case, yes, of course it could also be kin selection, the relatedness (Hamilton's original description) description of kin selection is really only useful in animals. In organisms with more lateral gene transfer they only need to share the gene in question, they could be completely unrelated in any other way. Indeed the paper even proposes this low but non-zero relatedness.

Now the big problem type 1

Type 1 is the traditional and first usage of the term group selection, but also the one only rarely proposed today, making it a very confusing term.

the big difference between kin selection and group selection (type 1) is that kin selection (or any form of selection including type 2) is about the selective advantage to the gene, an already well established principle, while many forms of group selection (type 1) propose a new "thing" on which selection occurs. what this thing is is never well defined but then neither were genes when natural selection was discovered.

To prove this form group selection and not kin selection you would have to show no selective advantage (or disadvantage) to the gene, basically you have to eliminate kin selection and other phenotypical expressions as a possibility. Proposed forms of group selection (type 2) can be shown to be products of normal gene based selection so you have to show this is not occurring. (thanks to Remi for this source). Intentional group formation in intelligent organisms (humans) is so far the only proposed mechanism in which this could work, and this would fall under memetics, which means it is occurring when related genetic differences are minor or non-existent.

Your paper does not show this form of selection, it does not even attempt to.

for a further breakdown of the diffrent forms of group selection I recommend this paper, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4850877/