Is it possible to view games made for Tandy Graphics (TGA, etc) on an IBM 5153 color display connected to an original Tandy 1000 (or 1000/A) in 16 colors?
CGA 40-column text mode is 320x200 16-colors and 80-column text mode is 640x200 16 colors. Those are a completely standard feature of CGA and therefore a completely normal thing for a CGA monitor to display. But because they're text mode, you can't set arbitrary pixels to arbitrary colors, you have to use the character cells.
Tandy and PCjr advanced graphics use the identical output resolutions, only with more freedom — the 2-color and 4-color modes allow any combination of 2 or 4 colors from the 16-color palette (unlike the CGA with its very limited palettes), and the 320x200 and (on the later TGA) 640x200 modes are available as full bitmapped graphics modes, meaning any pixel can be any color. Programmers care about this, but the monitor doesn't. It sees the same kind of signal that it would get from a CGA. Therefore any CGA RGBI monitor should be perfectly happy with Tandy graphics.
The Tandy 1000 CGA output was essentially like the IBM CGA electrically, and graphics modes were compatible. There was, however, an important difference in text mode. In text mode, the CGA used the middle 200 scan lines of a 262-line frame to display 25 rows of 8 scan lines each, with generous borders on the top and bottom. Using 8 lines per character meant that the bottom row of letters like "g" and "y" would touch the top row of letters like "E" and "T", which was less than ideal for legibility.
The Tandy 1000 shrinks the top and bottom borders by roughly 12-13 pixels, allowing the text portion of the screen to be expanded from 200 lines to 225 (9 scan lines per row). This substantially improves legibility on screens whose "vertical height" adjustment was set to leave at least 15 or so lines of border visible on the top and bottom. On screens which are adjusted to crop the border more closely to the text, the top and bottom of the Tandy text screen will get cut off.
I don't recall if the Tandy provided any way to use an 8-dot high font, but I wouldn't be surprised if it didn't. The "extra" line was added above the row of text, which meant that an inverse-video "E" would show one line of background above the text and one line below. That would also, however, mean that programming the CRT controller to use 8 dots instead of 9 would cause the bottom scan line of characters like "g" and "y" to be cut off entirely. Avoiding that would have required having a character set ROM which contained two character sets, and would also have required including a means of switching between them.
Basically yes. TGA (1000EX or similar) signal output (colour/intensity and sync signals) and connector pinout is upward compatible to CGA, thus compatible with CGA monitors. Both produce the very same RGBI signal using the same timing and encoding. TGA just employs more memory, thus being able to supply more colours at higher resolutions.
After all, TGA is basically a CGA with double the memory (32 KiB) and modes resulting from that - much like the IBM PCjr, which the Tandy 1000 was set against. The TGA II (Tandy 1000 SL/TL/RL and later) doubled that again to 64 KiB, finally enabling 640x200 in full 16 colours.
At least as long as colour mode is used. Text mode, when used in monochrome setup, is not. The monochrome setting is unique to TGA. Here a single B&W output signal is provided on pin 7, unused by CGA.