Tests should be taken when the student is ready to take them and can do well. It is not necessary to take them sophomore year, and most actually take tests in second semester junior or first semester senior year. The new SAT schedule starting next August, which takes away the Jan test but adds an August test, males it easier now to also wait until after junior year to take one or more of the tests.
The SAT is usually better taken after having math through at least most of pre-calc and and close to a few years of high school English, but some can perform well earlier. The current SAT practice test score, 1180, is a little better than average, and waiting a year could help bring it higher, but it is still a personal choice.
Subject tests should not be taken until you are prepared to do so; a recommended time is after having taken an applicable class so that studying for the test will not also involve relearing the course material. Math, particularly math 2 is best taken after having at least pre-calc. Important is that before deciding what you take, you find out first what is needed for colleges to which you intend to apply. For example, you mention UVA, VTech, and UMD. Well, none of those require any subject tests of regular applicants. Unless you are a home-schooled student, you do not need any subject tests for Vtech or UMD. UVa used to recommend two but has dropped that recommendation and now just says they are optional and may be considered, i.e., they are not necessary but you might consider sending two. Most colleges do not require, recommend, or consider subject tests for admission. There are in fact only 11 US colleges that strill require subject tests, all of them require only two and use the highest two if you submit more than two, and six of those take the ACT in lieu of both the SAT and subject tests. A number of other colleges recommend subject tests (usually two but Georgetown stands alone in recommending three). Some others, like UVA, neither require nor recommend them but will consider them if sent. Most of the applicable colleges are identitfied here: http://www.■■■■■■■■■■■■■■■/subject-test-requirements-and-recommendations/
As to what to take if you will be applying to a college for which you need subject tests, that also requires you to check the colleges requirements or recommendations. However, even without looking, you can assume most of the colleges that require or recommend subject tests want to see two (other than Georgetown which wants three), and if applying for enginering, they want to see: (a) a math, and some those insist on math 2, and (b) a science, either physics, chemistry, or biology, although some want a physics or chemistry rather than biology, e.g., Carnegie Mellon requires math 2 and physics or chemistry subject test for engineering. In other words, if engineering is seriously being considered and he will be applying to a school that needs subject tests, then he should seriously consider taking math 2 and either physics or chemistry because having those two subject tests will meet any and all subject test requirements or recommendations of all colleges that require or recommend subject tests for engineering.
As to the suggested latin test, it is of little to no use if applying for engineering. However, you need to look at whether the colleges he may apply to use language subject trests either for credit or placement after he has been admitted; some do.