Hi
These are very difficult questions with no definitive answers...
Tacitus informs us that in AD 23 there were nine Praetorian cohorts in service (Tac. Ann. IV. 5). Cassius Dio (Cass. Dio LV. 24. 6), however, wrote that Augustus had 10000 praetorians organised into ten units (= cohorts). Moreover there's the inscription from Lecce dei Marsi that you already mentioned and that indicates the existence of at least an eleventh Praetorian cohort. Now these are the information we have. What to do with it...?
From other inscriptions from Tiberius' reign it appears that at that time the Urban cohorts were numbered X, XI and XII in a direct continuation of the nine Praetorian cohorts. Cassius Dio is in this case may be extrapolating the situation of his own times (the end of 2. and beginning of 3. century) on the Augustan period. But S. J. Bingham suggested that perhaps he isn't wrong and the tenth unit which he wrote about may be the
speculatores, who were at that time organised into an independend unit and only later have been splitted into individual cohort. If this is the case, than it would make 9 Praetorian cohorts plus an unit of
speculatores, which would seem to match with Tacitus. Now the inscription from Lecce dei Marsi is about a certain Aulus Virgius Marsus who served as a tribune
in praetorio of Augustus and Tiberius:
...tr(ibuno) mil(itum) in praeto(rio) divi Aug(usti) et Ti(beri) Caesaris Aug(usti) cohort(ium) XI et IIII praetoriar(um)...
From this text we see that he was tribune of XIth and IIIIth Praetorian cohorts, which of course indicates that there were more than 9 cohorts at some time during Augustus' or Tiberius' reign. L. Keppie suggested a different amendment of this inscription, which would also allow for a different reading:
...tr(ibuno) mil(itum) in praeto(rio) divi Aug(usti) et Ti(beri) Caesaris Aug(usti) cohort(ium) XI et IIII praetori(ae)...
In this case we can read it so that Aulus Virgius Marsus was tribune in the XIth cohort (for that time perhaps without further name, but later to be called
urbana) and in the IIIIth Praetorian cohort. Than it would be possible to stay with the nine cohorts of Tacitus. But these are just theories and it's certainly possible that there were more Praetorian cohorts in service before AD 23. It is possible that from the beginning there were 12 Praetorian cohorts, 3 of which later became the Urban cohorts (X, XI, XII), as some scholars believe. Or it is possible, that Tiberius increased the number of cohorts shortly after the year AD 23. We cannot be sure here.
The question about the strength of these cohorts is similarly difficult with different scholars prefering 500 or 1000 men. As mentioned above, Cassius Dio wrote 10000 men in 10 units, which would mean 1000 men in a cohort. Tacitus (Tac. Hist. 93) told us that when Vitellius came to power he disbanded the old Guard and created a new one with 16 cohorts, each 1000 men strong. Some scholars do not agree with these numbers and prefer 500 men for a cohort. According to them Cassius Dio is similarly wrong with the number of men in cohorts as with the number of cohorts, extrapolating from his own times. Tacitus allegedly writes about this affair, because he wants to emphasize the novelties of the new emperor. M. Durry made calculations from the
laterculi praetorianum suggesting his 500 strong units, but his calculations have been quite forcibly questioned by D. L. Kennedy. The other argument of these scholars is the size of the Praetorian camp, which in comparison with camps on the
limes would suggest a garrison of only some 4000-6000 men. But some minor archaeological excavation of
castra praetoria showed that some of the buildings had more floors, that there were rooms inside the wall. This we cannot see in camps on
limes. Moreover some of the buildings typical for permanent border camps were not needed in Rome (because of the near city facilities) – for example
fabrica, valetudinarium, praetorium, principia, etc. and it is possible that some of them were missing in the
castra praetoria. Therefore the Praetorian camp could have housed much more men than one would expect. B. Rankov suggests ca. 12000 men, S. J. Bingham up to 15000. Therefore I think there's no strong reason to deny the numbers given by Cassius Dio and Tacitus and I'm on the 1000 men/cohort side, although this can change if some other evidence appears.
Reference:
Durry, M., 1938. Les cohortes pretoriennes, Paris. (unfortunately I haven't read this one, I know only some excerpts)
Durry, M., 1954. Praetoriae Cohortes, RE XXII 2, 1607-1634.
Bingham, S.J., 1997. The Praetorian Guard in the Political and Social Life of Julio-Claudian Rome (PhD thesis), Ottawa.
Kennedy, D.L., 1978. Some Observations on the Praetorian Guard. Ancient Society, 9, 275-301.
Keppie, L.J.F., 1996. The Praetorian Guard before Sejanus. Athenaeum, 84, 101-124.
Rankov, B., 2001. The Praetorian Guard, Oxford.
Hope this helps a little bit
Greetings
Alexandr