Western powers bar the USA tended to use radio comms at Platoon level and up, though this allowance mightn't have been met in second-string divisions. The USA was unique in making extensive use of hand-held FM squad radios, the "walkie-talkie" that became a byword. Radio use in the USSR was much more limited -- this was an industry where the Soviet Union was not a leader and it had neither enough wireless equipment nor suitable quality gear especially wrt ruggedness. Early on, only regiment/brigade HQs and up had radios, and even this wasn't universal. Later, Guards units and other top-line units might be allocated much more such equipment.

I don't know what bands ground force tactical radios usually employed, sorry. I can say that all forces preferentially employed field telephones when the situation permitted it (i.e. was static) because the problems of interception and location were understood.

Most naval vessels (probably also aircraft, but I'm not certain) used UHF communications because, unlike with VHF, triangulation could not be used to locate UHF transmitters in 1939. Germany was able to organise 'wolf-pack' U-boat attacks via radio for this reason with great success, but came to rely on it excessively and when the UK invented a device (HF/DF, known as 'Huff-Duff', based on a device called a goniometer) that could establish a bearing on UHF transmissions U-Boats began to suffer severe losses due to over-confident use of radio comms. In the final days of the war Germany was trying out a technique standard today called 'flash transmission' (a system known as 'Kurier') enabling ultra-rapid transmissions too brief to be located to get around this problem.

One ingenious idea was worked out by Hollywood actress Hedy Lamarr and her husband called spread spectrum -- the use of synchronised systems of transmitters/receivers that skipped from one frequency to another rapidly and (from the point of view of an eavesdropper) unpredictably, making either enemy jamming or interception very difficult to achieve. The US War department took no interest in the concept, a mistake because it was a perfectly sound idea that likewise became widely used from the 1960s onwards.

Were they given out at the company level?

Generally yes, this was often the lowest formation that would be given two-ways in Russian infantry units and German motorized units. American armored infantry also had dismountable radios at the company level. As a rule, the Germans, Americans and British all had radios at the platoon level as well in both armored and infantry formations. This wasn't often the case for regular Soviet infantry formations, largely due to doctrine: Whereas platoons were the smallest 'assault' unit in the other militaries, a Soviet company was considered the basic building block of an assaulting force.

HF? VHF? UHF?

No universal answer to this; certain air receivers for example came in VHF, some submarine two-ways and frequency findings came in HF and U/HF, and so on. Frequency very much was something relative to what the radio's purpose and intended range/battery life was.

Lastly, how did the different nations handle things like masts and repeater arrays? Modern western armies often set up masts which are easily portable by a single light vehicle, which is often a dedicated radio truck, was this the norm during the 2nd World War as well? Thanks!

The same principle applies, like this British example command truck and mast. Certain variants of armored cars could be used in a similar manner, as well as command tanks with radio sets that tied in to higher formations. However the establishment of more permanent or semi-permanent masts was also highly common, especially along the Atlantic wall defenses where the German formations were incredibly more static. Such wireless/radio arrangements were also often supported by redundant land-lines.