TL;DR no, yes, probably no
Go is a compiler+runtime. AFAIK any copyleft compiler worth using explicitly makes exceptions for its output and runtime, but the FSF says generally that the output of a GPL program is not also GPL[0]. If the runtime is AGPL (without such exception) and you link it into your program, your program is now considered a modified version of the AGPL runtime (e.g. it works exactly like the GPL in that linking is considered modifying). If your service interacts with users over a network, you have to offer the source of your modified program. Since you linked the runtime, you didn't even have to modify the Go source code to make an improvement (if there were an LAGPL, the linking could be OK unless you made the modification).
The other two cases are more ambiguous since they do deal with the ambiguous part of the license. The license says "interacting with it remotely through a computer network". However, it's not clear how much indirection is allowed, so you have to use some judgement. The FSF gives guidance [1]
> If a program is not expressly designed to interact with a user through a network, but is being run in an environment where it happens to do so, then it does not fall into this category.
However, I would be careful not to create a combined work that does interact with a user over a network in an attempt to circumvent this. E.g. a network proxy that was intimately tied to a non-networked program. See [2]
> By contrast, pipes, sockets and command-line arguments are communication mechanisms normally used between two separate programs. So when they are used for communication, the modules normally are separate programs. But if the semantics of the communication are intimate enough, exchanging complex internal data structures, that too could be a basis to consider the two parts as combined into a larger program.
Unless you consider the imagemagick command line arguments "complex internal data structures", it's probably difficult to run afoul of this.
For the Google search engine case, it depends on what degree the tooling interacts with users over a network. E.g. if it's part of an batch process to calculate rankings, it's not interacting with users over a network. If it's a backend that renders part of the results page for user requests, then probably yes. If it's crawl infrastructure that downloads pages on the web, probably no since that network interaction probably isn't considered to be with a user[3].
0: https://www.gnu.org/licenses/gpl-faq.html#WhatCaseIsOutputGP...
1: https://www.gnu.org/licenses/gpl-faq.html#AGPLv3InteractingR...
2: https://www.gnu.org/licenses/gpl-faq.html#MereAggregation
3: https://www.gnu.org/licenses/gpl-faq.html#AGPLv3ServerAsUser