We present submillimeter observations of the Local Group, metal-poor, irregular dwarf galaxy IC 10, directly relevant to the interaction between interstellar medium (ISM) and star formation activity in primeval galaxies. Using the James Clerk Maxwell Telescope, we have observed the fine-structure neutral carbon transition P-3(1) --> P-3(0) at 492 GHz and the rotational J = 3 --> 2 transition of (CO)-C-12 and (CO)-C-13, the most massive giant molecular cloud complex in this galaxy, IC 10-SE. We find that, although the IC I-[CII]/I-CO ratio for this object is a factor of 4 larger than the typical Milky Way value, its [C I] to CO intensity ratio I-[C I]/I-CO similar or equal to 18 +/- 2 (in units of ergs s(-1) cm(-2) sr(-1)) is similar (only about 50% larger) to that of the Milky Way. Modelling of the behavior of the [C II]/CO and [C I]/CO intensity ratios with metallicity indicates that, if C+ and C-0 are chiefly produced by UV photodissociation in the hotodissociation region, both ratios should increase sharply with decreasing metallicity (and consequently diminished UV shielding). These data then suggest a different origin for an important fraction of CO in these clouds, unrelated to photodissociation. We have also mapped the 850 mu m continuum in this region using the Submillimetre Common User Bolometer Array. Employing these data in conjunction with KAO and IRAM measurements we find that the 100-1300 mu m continuum emission corresponds to a graybody with an extremely low emissivity exponent, beta similar to 0.5. We conclude that this low exponent is most likely due to the destruction of small dust grains, brought about by the increased penetration of UV radiation in the low-metallicity ISM. If a low emissivity exponent in the submillimeter is a general property of metal-poor systems, then the interpretation of millimeter and submillimeter surveys of high-z galaxies should be revised.