Are we allowed to submit ROM hacks/texture edits of existing games?

In short, yes, assuming by "ROM hacks" you mean editing SmileBASIC games. Here's SmileBoom's policy on this.

独自ルールを設けた公開キーの頒布について 昨今、独自の利用ルールを設けて公開キーを頒布するケースが報告されており、その対応について混乱が生じているケースも散見されます。 正しく公開キーを取り扱っていただけるよう、改めて、公開キーによって公開されるプログラムなどの取り扱いについて説明いたします。 自作のプログラムなどを他のユーザーに対して公開する場合、公開されるプログラムが二次的に利用されることを許諾することで公開キーが発行されます。 よって、仮に、公開キーの所有者がいかなるルールを設けたとしても、発行された公開キーは第三者による二次利用を許諾されている状態に変わりはなく、その公開キーを利用される利用者（第三者）は、二次利用が許諾されている前提で利用されることに問題はありません。

Regarding Public Keys Distributed with Unique Rules Recently, cases have been reported of public keys being distributed with unique rules for use, and cases have also been seen of confusion resulting from that correspondence. In order to handle public keys correctly, once again, we will explain regarding the handling of programs, etc. published by public key. When publishing your own programs, etc. for other users, a public key is issued when you grant permission for secondary use of your published program. Consequently, for the time being, regardless of any kind of rule the public key's owner sets, it does not change the fact that permission has been granted for secondary use by third parties of the issued public key, and for a user (third party) who uses that public key, there is no problem in using it under the assumption that secondary use is permitted.

There's also the agreement screen shown when publishing a project in SmileBASIC:

Confirm agreement to the terms of publication Inappropriate content will be deleted without notice. When submitting, you must warrant that your project is your own original work and does not contain any unauthorized 3rd party content, personally identifiable information or inappropriate content such as offensive words, images or audio. For more details, refer to the official website. Please note that all published files are deemed to be permitted for secondary use by others Do you agree to the above terms? [No] [Yes]

And this section of the online manual:

Once you publish a project, anyone in the world who owns this product and has been given the Public Key can view your work (program, data, etc.). Please be sure not to carelessly publish projects that contain libelous content or personally identifiable information such as addresses and telephone numbers. Such content, if distributed by a malicious user to the general public via the Internet, might ruin the life of the person involved. Please also note that programs and resources (images and sounds) included in published projects are deemed to have been provided by their creators with permission for secondary use by third parties. Please be careful to avoid problems such as infringement of copyright. If a published project is the subject of a takedown notice, SmileBoom Co., Ltd. may delete the relevant project without prior notice.

The wording is a bit vague, but what it seems to boil down to is that you retain copyright of everything you make in SmileBASIC, but upon publishing you issue an irrevocable license for anyone to use, modify, and/or distribute those works (presumably only within SmileBASIC itself). So, it's okay to use any resources from SmileBASIC projects freely in your own SmileBASIC project, even if the author says otherwise, as long as they're not infringing on copyright in the first place (like sprites from Mario or something).