What you say in your edit, Maizi Wu, is indeed relevant to clarify your question ("I'd like to make my question clear that it is not quite about the passive periphrastic, but the common passive usage of the verb"). Essentially, the answer to your question (and, in fact, to all your three subquestions) is that both examples Reī frūmentāriae prōspicitur ā Caesare and ... Reī frūmentāriae (sibi: i.e. Caesarī) prōspiciendum (esse) exīstimāvit involve an impersonal construction, i.e. both examples lack a subject.
Your first subquestion ("Why is the dative also used in passive voice as the subject?") wrongly presupposes that these two constructions must have a subject but here we deal with two impersonal constructions, i.e. both lack a subject (NB: the dative complement reī frūmentāriae has the very same syntactic status in the active and passive constructions).
Your second subquestion ("Why is the participle prōspiciendum in neutral gender?) has a related answer: it is in neutral gender because the construction is impersonal.
Finally, your third subquestion ("If converting rēbus frūmentāriīs plural, what gender and number should prōspiciendum be?") has, again, the same answer: the construction lacks a subject. If you convert the dative complement to plural, the gender and number of the -nd- form remain the same. Why? Because, again, the dative is not the subject.
As you can see, all your three subquestions revolve around the same: the construction is impersonal. So don't expect to find a subject there. Descriptively speaking, there is none!
Once it is clarified that both examples in bold above are impersonal constructions (i.e. they lack a subject), one can wonder if these two examples are equally passive (I know this is not your question, but I can't help saying something more on this related issue as well).
Let's start with the the "easy" case. Descriptively speaking, your (invented but correct) passive construction Reī frūmentāriae prōspicitur ā Caesare lacks a subject, whereby, as noted, it is called impersonal. Impersonal passives are typically made out of agentive intransitive verbs (or agentive transitive verbs that are used intransitively): the so-called "unergative verbs". You can find some hopefully useful discussion of Latin impersonal passives in this link. For the purposes of building an impersonal passive, the issue whether the intransitive verb takes a dative argument or not is mostly irrelevant (NB: as for why I say "mostly" here (rather than "always"), see the brief discussion on the example in (1) below, which is also alluded to in my comment to Joonas's answer).
Now let's deal with the "tricky" case. Don't get suprised if you see that people often concentrate/comment on the passive or active role of the -nd- form of your example from Caesar: ... reī frūmentāriae (sibi: i.e. Caesarī) prōspiciendum (esse) exīstimāvit. This is partly due to an unsolved debate (even in the current specialized literature) about the traditional concept of "passive periphrastic". See this link for a brief discussion.
Here is a synthesis of my personal view:
Impersonal constructions with -nd- forms can be passive (see ex. (1) with an "ablative of agent": est a vobis... consulendum) or not (see ex. (2) with the so-called, in fact, miscalled, "dative of agent": moriendum est omnibus; NB: in this case, the lack of passivization is even more evident because mori is an unaccusative verb: as rightly noted in this wiki link, unaccusative verbs (i.e. those intransitive verbs that are not agentive) do not typically form impersonal passives):
(1) Aguntur bona multorum civium quibus est a vobis et ipsorum causa et rei publicae consulendum. (Cic. Manil. 6) ‘The property of many citizens is at stake, which you ought greatly to regard, both for your own sake, and for that of the republic.’ (C. D. Yonge, 1856, Perseus)
(2) moriendum est enim omnibus (Cic. Tusc. 1, 9, 15) ‘All must indeed die.’
Finally, as for your initial example from Caesar,
(3) rei frumentariae prospiciendum existimavit (Caes. Gal. 1.23)
it would be an excellent question to ask whether prospiciendum (esse) in this particular example is a passive form. Here I tend to agree with Sebastian's comment to Davide's answer and with Joonas's answer: prospiciendum (esse) is an impersonal construction but it is not a passive construction. The basics of my argumentation can be found in this link, which is, indeed, a bit long but, you know, the answer is not an easy one... [NB: Pinkster's (2015) (correct) observation/conclusion in his Oxford Latin Syntax that gerundives are "more frequently active" should not go unnoticed since it goes against what is often found in many traditional grammars of Latin. See also Danesi, Johnson, and Barðdal (2017), who also offer an interesting critique of the traditional claim that a typical gerundive (-nd-) construction with esse is a passive construction. In my opinion, this paper by Danesi et al. is excellent but, unfortunately, they do not take into account the relevance of examples like (1), which contain an ablative of agent. In my opinion, examples like (1) are passive. NB: the typical account that an ablative of agent (a vobis) is used there instead of a "dative of agent" (vobis) to avoid the ambiguity with the other dative (quibus) only offers a partial solution. Similarly, Danesi et al. would also have problems to account for the following examples in (4) and (5), which are clearly passive. In contrast to the example in (1), note that their ablatives of agent (a consulibus & ab oratore) do not seem to be used there because of an ambiguity problem (that's why I said that the typical account of why an ablative of agent is used in (1) is partial):
(4) Sed tamen et Crassus a consulibus meam causam suscipiendam esse dicebat. (Cic. Sest. 41)
(5) Ergo haec et agenda sunt ab oratore, quae explicauit Antonius, et dicenda quodam modo (Cic. De Or. 3, 10, 37).
